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| optimization under constraints: Optimization with PDE Constraints Michael Hinze, Rene Pinnau, Michael Ulbrich, Stefan Ulbrich, 2010-10-28 Solving optimization problems subject to constraints given in terms of partial d- ferential equations (PDEs) with additional constraints on the controls and/or states is one of the most challenging problems in the context of industrial, medical and economical applications, where the transition from model-based numerical si- lations to model-based design and optimal control is crucial. For the treatment of such optimization problems the interaction of optimization techniques and num- ical simulation plays a central role. After proper discretization, the number of op- 3 10 timization variables varies between 10 and 10 . It is only very recently that the enormous advances in computing power have made it possible to attack problems of this size. However, in order to accomplish this task it is crucial to utilize and f- ther explore the speci?c mathematical structure of optimization problems with PDE constraints, and to develop new mathematical approaches concerning mathematical analysis, structure exploiting algorithms, and discretization, with a special focus on prototype applications. The present book provides a modern introduction to the rapidly developing ma- ematical ?eld of optimization with PDE constraints. The ?rst chapter introduces to the analytical background and optimality theory for optimization problems with PDEs. Optimization problems with PDE-constraints are posed in in?nite dim- sional spaces. Therefore, functional analytic techniques, function space theory, as well as existence- and uniqueness results for the underlying PDE are essential to study the existence of optimal solutions and to derive optimality conditions. |
| optimization under constraints: Constraint Processing Rina Dechter, 2003-05-05 Constraint reasoning has matured over the last three decades with contributions from a diverse community of researchers in artificial intelligence, databases and programming languages, operations research, management science, and applied mathematics. In Constraint Processing, Rina Dechter synthesizes these contributions, as well as her own significant work, to provide the first comprehensive examination of the theory that underlies constraint processing algorithms. |
| optimization under constraints: Optimization with Disjunctive Constraints H.D. Sherali, C.M. Shetty, 2012-12-06 The disjunctive cut principle of Balas and Jeroslow, and the related polyhedral annexation principle of Glover, provide new insights into cutting plane theory. This has resulted in its ability to not only subsume many known valid cuts but also improve upon them. Originally a set of notes were written for the purpose of putting together in a common terminology and framework significant results of Glover and others using a geometric approach, referred to in the literature as convexity cuts, and the algebraic approach of Balas and Jeroslow known as Disjunctive cuts. As it turned out subsequently the polyhedral annexation approach of Glover is also closely connected with the basic disjunctive principle of Balas and Jeroslow. In this monograph we have included these results and have also added several published results which seem to be of strong interest to researchers in the area of developing strong cuts for disjunctive programs. In particular, several results due to Balas [4,5,6,7], Glover [18,19] and Jeroslow [23,25,26] have been used in this monograph. The appropriate theorems are given without proof. The notes also include several results yet to be published [32,34,35] obtained under a research contract with the National Science Foundation to investigate solution methods for disjunctive programs. The monograph is self-contained and complete in the sense that it attempts to pool together existing results which the authors viewed as important to future research on optimization using the disjunctive cut approach. |
| optimization under constraints: Global Optimization with Non-Convex Constraints Roman G. Strongin, Yaroslav D. Sergeyev, 2013-11-09 Everything should be made as simple as possible, but not simpler. (Albert Einstein, Readers Digest, 1977) The modern practice of creating technical systems and technological processes of high effi.ciency besides the employment of new principles, new materials, new physical effects and other new solutions ( which is very traditional and plays the key role in the selection of the general structure of the object to be designed) also includes the choice of the best combination for the set of parameters (geometrical sizes, electrical and strength characteristics, etc.) concretizing this general structure, because the Variation of these parameters ( with the structure or linkage being already set defined) can essentially affect the objective performance indexes. The mathematical tools for choosing these best combinations are exactly what is this book about. With the advent of computers and the computer-aided design the pro bations of the selected variants are usually performed not for the real examples ( this may require some very expensive building of sample op tions and of the special installations to test them ), but by the analysis of the corresponding mathematical models. The sophistication of the mathematical models for the objects to be designed, which is the natu ral consequence of the raising complexity of these objects, greatly com plicates the objective performance analysis. Today, the main (and very often the only) available instrument for such an analysis is computer aided simulation of an object's behavior, based on numerical experiments with its mathematical model. |
| optimization under constraints: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints Jiri Outrata, M. Kocvara, J. Zowe, 2013-06-29 In the early fifties, applied mathematicians, engineers and economists started to pay c10se attention to the optimization problems in which another (lower-Ievel) optimization problem arises as a side constraint. One of the motivating factors was the concept of the Stackelberg solution in game theory, together with its economic applications. Other problems have been encountered in the seventies in natural sciences and engineering. Many of them are of practical importance and have been extensively studied, mainly from the theoretical point of view. Later, applications to mechanics and network design have lead to an extension of the problem formulation: Constraints in form of variation al inequalities and complementarity problems were also admitted. The term generalized bi level programming problems was used at first but later, probably in Harker and Pang, 1988, a different terminology was introduced: Mathematical programs with equilibrium constraints, or simply, MPECs. In this book we adhere to MPEC terminology. A large number of papers deals with MPECs but, to our knowledge, there is only one monograph (Luo et al. , 1997). This monograph concentrates on optimality conditions and numerical methods. Our book is oriented similarly, but we focus on those MPECs which can be treated by the implicit programming approach: the equilibrium constraint locally defines a certain implicit function and allows to convert the problem into a mathematical program with a nonsmooth objective. |
| optimization under constraints: Control and Optimization with Differential-Algebraic Constraints Lorenz T. Biegler, Stephen L. Campbell, Volker Mehrmann, 2012-11-01 A cutting-edge guide to modelling complex systems with differential-algebraic equations, suitable for applied mathematicians, engineers and computational scientists. |
| optimization under constraints: Optimization Under Constraints Peter Whittle, 1990 |
| optimization under constraints: Practical Optimization Andreas Antoniou, Wu-Sheng Lu, 2007-12-14 Practical Optimization: Algorithms and Engineering Applications provides a hands-on treatment of the subject of optimization. A comprehensive set of problems and exercises makes the book suitable for use in one or two semesters of a first-year graduate course or an advanced undergraduate course. Each half of the book contains a full semester’s worth of complementary yet stand-alone material. The practical orientation of the topics chosen and a wealth of useful examples also make the book suitable for practitioners in the field. Advancements in the efficiency of digital computers and the evolution of reliable software for numerical computation during the past three decades have led to a rapid growth in the theory, methods, and algorithms of numerical optimization. This body of knowledge has motivated widespread applications of optimization methods in many disciplines, e.g., engineering, business, and science, and has subsequently led to problem solutions that were considered intractable not too long ago. |
| optimization under constraints: Numerical PDE-Constrained Optimization Juan Carlos De los Reyes, 2015-03-05 This book introduces, in an accessible way, the basic elements of Numerical PDE-Constrained Optimization, from the derivation of optimality conditions to the design of solution algorithms. Numerical optimization methods in function-spaces and their application to PDE-constrained problems are carefully presented. The developed results are illustrated with several examples, including linear and nonlinear ones. In addition, MATLAB codes, for representative problems, are included. Furthermore, recent results in the emerging field of nonsmooth numerical PDE constrained optimization are also covered. The book provides an overview on the derivation of optimality conditions and on some solution algorithms for problems involving bound constraints, state-constraints, sparse cost functionals and variational inequality constraints. |
| optimization under constraints: Optimization Under Constraints Peter Whittle, 1971 First thoughts on maximization; Constrained maximization and lagrangian methods; The strong lagrangian principle: convexity; Linear programming; Some particular linear problems; Some problems with linear constraints; Nonlinear constraints, and stochastic effects; Numerical methods; Vector maximization problems. |
| optimization under constraints: Constrained Optimization and Lagrange Multiplier Methods Dimitri P. Bertsekas, 1996 |
| optimization under constraints: Real-time PDE-constrained Optimization Lorenz T. Biegler, Omar Ghattas, Matthias Heinkenschloss, David Keyes, Bart van Bloemen Waanders, 2007-01-01 Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs--and the requirement for rapid solution--pose significant difficulties. A particularly challenging class of PDE-constrained optimization problems is characterized by the need for real-time solution, i.e., in time scales that are sufficiently rapid to support simulation-based decision making. Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. In addition to presenting state-of-the-art algorithms and formulations, the text illustrates these algorithms with a diverse set of applications that includes problems in the areas of aerodynamics, biology, fluid dynamics, medicine, chemical processes, homeland security, and structural dynamics. Audience: readers who have expertise in simulation and are interested in incorporating optimization into their simulations, who have expertise in numerical optimization and are interested in adapting optimization methods to the class of infinite-dimensional simulation problems, or who have worked in offline optimization contexts and are interested in moving to online optimization. |
| optimization under constraints: Optimal Structural Design under Stability Constraints Antoni Gajewski, Michal Zyczkowski, 2012-12-06 The first optimal design problem for an elastic column subject to buckling was formulated by Lagrange over 200 years ago. However, rapid development of structural optimization under stability constraints occurred only in the last twenty years. In numerous optimal structural design problems the stability phenomenon becomes one of the most important factors, particularly for slender and thin-walled elements of aerospace structures, ships, precision machines, tall buildings etc. In engineering practice stability constraints appear more often than it might be expected; even when designing a simple beam of constant width and variable depth, the width - if regarded as a design variable - is finally determined by a stability constraint (lateral stability). Mathematically, optimal structural design under stability constraints usually leads to optimization with respect to eigenvalues, but some cases fall even beyond this type of problems. A total of over 70 books has been devoted to structural optimization as yet, but none of them has treated stability constraints in a sufficiently broad and comprehensive manner. The purpose of the present book is to fill this gap. The contents include a discussion of the basic structural stability and structural optimization problems and the pertinent solution methods, followed by a systematic review of solutions obtained for columns, arches, bar systems, plates, shells and thin-walled bars. A unified approach based on Pontryagin's maximum principle is employed inasmuch as possible, at least to problems of columns, arches and plates. Parametric optimization is discussed as well. |
| optimization under constraints: Algorithms for Optimization Mykel J. Kochenderfer, Tim A. Wheeler, 2019-03-12 A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals. |
| optimization under constraints: Linear and Integer Optimization Gerard Sierksma, Yori Zwols, 2015-05-01 Presenting a strong and clear relationship between theory and practice, Linear and Integer Optimization: Theory and Practice is divided into two main parts. The first covers the theory of linear and integer optimization, including both basic and advanced topics. Dantzig's simplex algorithm, duality, sensitivity analysis, integer optimization models |
| optimization under constraints: Stochastic Recursive Algorithms for Optimization S. Bhatnagar, H.L. Prasad, L.A. Prashanth, 2012-08-12 Stochastic Recursive Algorithms for Optimization presents algorithms for constrained and unconstrained optimization and for reinforcement learning. Efficient perturbation approaches form a thread unifying all the algorithms considered. Simultaneous perturbation stochastic approximation and smooth fractional estimators for gradient- and Hessian-based methods are presented. These algorithms: • are easily implemented; • do not require an explicit system model; and • work with real or simulated data. Chapters on their application in service systems, vehicular traffic control and communications networks illustrate this point. The book is self-contained with necessary mathematical results placed in an appendix. The text provides easy-to-use, off-the-shelf algorithms that are given detailed mathematical treatment so the material presented will be of significant interest to practitioners, academic researchers and graduate students alike. The breadth of applications makes the book appropriate for reader from similarly diverse backgrounds: workers in relevant areas of computer science, control engineering, management science, applied mathematics, industrial engineering and operations research will find the content of value. |
| optimization under constraints: Large-Scale PDE-Constrained Optimization Lorenz T. Biegler, Omar Ghattas, Matthias Heinkenschloss, Bart van Bloemen Waanders, 2012-12-06 Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDE-constrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDE-based optimization. The chapters in this volume collectively assess the state of the art in PDE-constrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research. |
| optimization under constraints: Engineering Design Optimization Joaquim R. R. A. Martins, Andrew Ning, 2021-11-18 Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-semester graduate course on optimization in aerospace, civil, mechanical, electrical, and chemical engineering departments. |
| optimization under constraints: Robust Optimization Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski, 2009-08-10 Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject. |
| optimization under constraints: Deterministic Global Optimization Christodoulos A. Floudas, 2013-03-09 The vast majority of important applications in science, engineering and applied science are characterized by the existence of multiple minima and maxima, as well as first, second and higher order saddle points. The area of Deterministic Global Optimization introduces theoretical, algorithmic and computational ad vances that (i) address the computation and characterization of global minima and maxima, (ii) determine valid lower and upper bounds on the global minima and maxima, and (iii) address the enclosure of all solutions of nonlinear con strained systems of equations. Global optimization applications are widespread in all disciplines and they range from atomistic or molecular level to process and product level representations. The primary goal of this book is three fold : first, to introduce the reader to the basics of deterministic global optimization; second, to present important theoretical and algorithmic advances for several classes of mathematical prob lems that include biconvex and bilinear; problems, signomial problems, general twice differentiable nonlinear problems, mixed integer nonlinear problems, and the enclosure of all solutions of nonlinear constrained systems of equations; and third, to tie the theory and methods together with a variety of important applications. |
| optimization under constraints: Optimization Theory and Methods Wenyu Sun, Ya-Xiang Yuan, 2006-05-24 Optimization Theory and Methods can be used as a textbook for an optimization course for graduates and senior undergraduates. It is the result of the author's teaching and research over the past decade. It describes optimization theory and several powerful methods. For most methods, the book discusses an idea’s motivation, studies the derivation, establishes the global and local convergence, describes algorithmic steps, and discusses the numerical performance. |
| optimization under constraints: Nonlinear Optimization of Vehicle Safety Structures Jesper Christensen, Christophe Bastien, 2015-12-07 Nonlinear Optimization of Vehicle Safety Structures: Modeling of Structures Subjected to Large Deformations provides a cutting-edge overview of the latest optimization methods for vehicle structural design. The book focuses on large deformation structural optimization algorithms and applications, covering the basic principles of modern day topology optimization and comparing the benefits and flaws of different algorithms in use. The complications of non-linear optimization are highlighted, along with the shortcomings of recently proposed algorithms. Using industry relevant case studies, users will how optimization software can be used to address challenging vehicle safety structure problems and how to explore the limitations of the approaches given. The authors draw on research work with the likes of MIRA, Jaguar Land Rover and Tata Motors European Technology Centre as part of multi-million pound European funded research projects, emphasizing the industry applications of recent advances. The book is intended for crash engineers, restraints system engineers and vehicle dynamics engineers, as well as other mechanical, automotive and aerospace engineers, researchers and students with a structural focus. - Focuses on non-linear, large deformation structural optimization problems relating to vehicle safety - Discusses the limitations of different algorithms in use and offers guidance on best practice approaches through the use of relevant case studies - Author's present research from the cutting-edge of the industry, including research from leading European automotive companies and organizations - Uses industry relevant case studies, allowing users to understand how optimization software can be used to address challenging vehicle safety structure problems and how to explore the limitations of the approaches given |
| optimization under constraints: Linear Programming Robert J Vanderbei, 2013-07-16 This Fourth Edition introduces the latest theory and applications in optimization. It emphasizes constrained optimization, beginning with a substantial treatment of linear programming and then proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Readers will discover a host of practical business applications as well as non-business applications. Topics are clearly developed with many numerical examples worked out in detail. Specific examples and concrete algorithms precede more abstract topics. With its focus on solving practical problems, the book features free C programs to implement the major algorithms covered, including the two-phase simplex method, primal-dual simplex method, path-following interior-point method, and homogeneous self-dual methods. In addition, the author provides online JAVA applets that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows. These C programs and JAVA tools can be found on the book's website. The website also includes new online instructional tools and exercises. |
| optimization under constraints: Joint Source-Channel Decoding Pierre Duhamel, Michel Kieffer, 2009-11-26 - Treats joint source and channel decoding in an integrated way - Gives a clear description of the problems in the field together with the mathematical tools for their solution - Contains many detailed examples useful for practical applications of the theory to video broadcasting over mobile and wireless networks Traditionally, cross-layer and joint source-channel coding were seen as incompatible with classically structured networks but recent advances in theory changed this situation. Joint source-channel decoding is now seen as a viable alternative to separate decoding of source and channel codes, if the protocol layers are taken into account. A joint source/protocol/channel approach is thus addressed in this book: all levels of the protocol stack are considered, showing how the information in each layer influences the others. This book provides the tools to show how cross-layer and joint source-channel coding and decoding are now compatible with present-day mobile and wireless networks, with a particular application to the key area of video transmission to mobiles. Typical applications are broadcasting, or point-to-point delivery of multimedia contents, which are very timely in the context of the current development of mobile services such as audio (MPEG4 AAC) or video (H263, H264) transmission using recent wireless transmission standards (DVH-H, DVB-SH, WiMAX, LTE). This cross-disciplinary book is ideal for graduate students, researchers, and more generally professionals working either in signal processing for communications or in networking applications, interested in reliable multimedia transmission. This book is also of interest to people involved in cross-layer optimization of mobile networks. Its content may provide them with other points of view on their optimization problem, enlarging the set of tools which they could use. Pierre Duhamel is director of research at CNRS/ LSS and has previously held research positions at Thomson-CSF, CNET, and ENST, where he was head of the Signal and Image Processing Department. He has served as chairman of the DSP committee and associate Editor of the IEEE Transactions on Signal Processing and Signal Processing Letters, as well as acting as a co-chair at MMSP and ICASSP conferences. He was awarded the Grand Prix France Telecom by the French Science Academy in 2000. He is co-author of more than 80 papers in international journals, 250 conference proceedings, and 28 patents. Michel Kieffer is an assistant professor in signal processing for communications at the Université Paris-Sud and a researcher at the Laboratoire des Signaux et Systèmes, Gif-sur-Yvette, France. His research interests are in joint source-channel coding and decoding techniques for the reliable transmission of multimedia contents. He serves as associate editor of Signal Processing (Elsevier). He is co-author of more than 90 contributions to journals, conference proceedings, and book chapters. - Treats joint source and channel decoding in an integrated way - Gives a clear description of the problems in the field together with the mathematical tools for their solution - Contains many detailed examples useful for practical applications of the theory to video broadcasting over mobile and wireless networks |
| optimization under constraints: An Introduction to Optimization Edwin K. P. Chong, Stanislaw H. Żak, 2013-02-05 Praise for the Third Edition . . . guides and leads the reader through the learning path . . . [e]xamples are stated very clearly and the results are presented with attention to detail. —MAA Reviews Fully updated to reflect new developments in the field, the Fourth Edition of Introduction to Optimization fills the need for accessible treatment of optimization theory and methods with an emphasis on engineering design. Basic definitions and notations are provided in addition to the related fundamental background for linear algebra, geometry, and calculus. This new edition explores the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. The authors also present an optimization perspective on global search methods and include discussions on genetic algorithms, particle swarm optimization, and the simulated annealing algorithm. Featuring an elementary introduction to artificial neural networks, convex optimization, and multi-objective optimization, the Fourth Edition also offers: A new chapter on integer programming Expanded coverage of one-dimensional methods Updated and expanded sections on linear matrix inequalities Numerous new exercises at the end of each chapter MATLAB exercises and drill problems to reinforce the discussed theory and algorithms Numerous diagrams and figures that complement the written presentation of key concepts MATLAB M-files for implementation of the discussed theory and algorithms (available via the book's website) Introduction to Optimization, Fourth Edition is an ideal textbook for courses on optimization theory and methods. In addition, the book is a useful reference for professionals in mathematics, operations research, electrical engineering, economics, statistics, and business. |
| optimization under constraints: Probabilistic and Randomized Methods for Design under Uncertainty Giuseppe Calafiore, Fabrizio Dabbene, 2006-03-06 In many engineering design and optimization problems, the presence of uncertainty in the data is a critical issue. There are different ways to describe this uncertainty and to devise designs that are partly insensitive or robust to it. This book examines uncertain systems in control engineering and general decision or optimization problems for which data is uncertain. Written by leading researchers in optimization and robust control; it highlights the interactions between these two fields. Part I describes theory and solution methods for probability-constrained and stochastic optimization problems; Part II focuses on numerical methods for solving randomly perturbed convex programs and semi-infinite optimization problems by probabilistic techniques; Part III details the theory and applications of randomized techniques to the analysis and design of robust control systems. It will interest researchers, academics and postgraduates in control engineering and operations research as well as professionals working in operations research. |
| optimization under constraints: Decision Making under Constraints Martine Ceberio, Vladik Kreinovich, 2020-03-24 This book presents extended versions of selected papers from the annual International Workshops on Constraint Programming and Decision Making from 2016 to 2018. The papers address all stages of decision-making under constraints: (1) precisely formulating the problem of multi-criteria decision-making; (2) determining when the corresponding decision problem is algorithmically solvable; (3) finding the corresponding algorithms and making these algorithms as efficient as possible; and (4) taking into account interval, probabilistic, and fuzzy uncertainty inherent in the corresponding decision-making problems. In many application areas, it is necessary to make effective decisions under constraints, and there are several area-specific techniques for such decision problems. However, because they are area-specific, it is not easy to apply these techniques in other application areas. As such, the annual International Workshops on Constraint Programming and Decision Making focus on cross-fertilization between different areas, attracting researchers and practitioners from around the globe. The book includes numerous papers describing applications, in particular, applications to engineering, such as control of unmanned aerial vehicles, and vehicle protection against improvised explosion devices. |
| optimization under constraints: Trust Region Methods A. R. Conn, N. I. M. Gould, Ph. L. Toint, 2000-01-01 This is the first comprehensive reference on trust-region methods, a class of numerical algorithms for the solution of nonlinear convex optimization methods. Its unified treatment covers both unconstrained and constrained problems and reviews a large part of the specialized literature on the subject. It also provides an up-to-date view of numerical optimization. |
| optimization under constraints: Lagrange Multiplier Approach to Variational Problems and Applications Kazufumi Ito, Karl Kunisch, 2008-01-01 Lagrange multiplier theory provides a tool for the analysis of a general class of nonlinear variational problems and is the basis for developing efficient and powerful iterative methods for solving these problems. This comprehensive monograph analyzes Lagrange multiplier theory and shows its impact on the development of numerical algorithms for problems posed in a function space setting. The authors develop and analyze efficient algorithms for constrained optimization and convex optimization problems based on the augumented Lagrangian concept and cover such topics as sensitivity analysis, convex optimization, second order methods, and shape sensitivity calculus. General theory is applied to challenging problems in optimal control of partial differential equations, image analysis, mechanical contact and friction problems, and American options for the Black-Scholes model. |
| optimization under constraints: 22nd European Symposium on Computer Aided Process Engineering David Bogle, 2012-08-03 Computer aided process engineering (CAPE) plays a key design and operations role in the process industries. This conference features presentations by CAPE specialists and addresses strategic planning, supply chain issues and the increasingly important area of sustainability audits. Experts collectively highlight the need for CAPE practitioners to embrace the three components of sustainable development: environmental, social and economic progress and the role of systematic and sophisticated CAPE tools in delivering these goals. Contributions from the international community of researchers and engineers using computing-based methods in process engineering Review of the latest developments in process systems engineering Emphasis on a systems approach in tackling industrial and societal grand challenges |
| optimization under constraints: Introduction to Optimum Design Jasbir Singh Arora, 2011-08-12 Introduction to Optimum Design, Third Edition describes an organized approach to engineering design optimization in a rigorous yet simplified manner. It illustrates various concepts and procedures with simple examples and demonstrates their applicability to engineering design problems. Formulation of a design problem as an optimization problem is emphasized and illustrated throughout the text. Excel and MATLAB® are featured as learning and teaching aids. - Basic concepts of optimality conditions and numerical methods are described with simple and practical examples, making the material highly teachable and learnable - Includes applications of optimization methods for structural, mechanical, aerospace, and industrial engineering problems - Introduction to MATLAB Optimization Toolbox - Practical design examples introduce students to the use of optimization methods early in the book - New example problems throughout the text are enhanced with detailed illustrations - Optimum design with Excel Solver has been expanded into a full chapter - New chapter on several advanced optimum design topics serves the needs of instructors who teach more advanced courses |
| optimization under constraints: Optimization Models Giuseppe C. Calafiore, Laurent El Ghaoui, 2014-10-31 This accessible textbook demonstrates how to recognize, simplify, model and solve optimization problems - and apply these principles to new projects. |
| optimization under constraints: Nature-Inspired Optimization Algorithms Xin-She Yang, 2014-02-17 Nature-Inspired Optimization Algorithms provides a systematic introduction to all major nature-inspired algorithms for optimization. The book's unified approach, balancing algorithm introduction, theoretical background and practical implementation, complements extensive literature with well-chosen case studies to illustrate how these algorithms work. Topics include particle swarm optimization, ant and bee algorithms, simulated annealing, cuckoo search, firefly algorithm, bat algorithm, flower algorithm, harmony search, algorithm analysis, constraint handling, hybrid methods, parameter tuning and control, as well as multi-objective optimization. This book can serve as an introductory book for graduates, doctoral students and lecturers in computer science, engineering and natural sciences. It can also serve a source of inspiration for new applications. Researchers and engineers as well as experienced experts will also find it a handy reference. - Discusses and summarizes the latest developments in nature-inspired algorithms with comprehensive, timely literature - Provides a theoretical understanding as well as practical implementation hints - Provides a step-by-step introduction to each algorithm |
| optimization under constraints: 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering , 2015-07-14 25th European Symposium on Computer-Aided Process Engineering contains the papers presented at the 12th Process Systems Engineering (PSE) and 25th European Society of Computer Aided Process Engineering (ESCAPE) Joint Event held in Copenhagen, Denmark, 31 May - 4 June 2015. The purpose of these series is to bring together the international community of researchers and engineers who are interested in computing-based methods in process engineering. This conference highlights the contributions of the PSE/CAPE community towards the sustainability of modern society. Contributors from academia and industry establish the core products of PSE/CAPE, define the new and changing scope of our results, and future challenges. Plenary and keynote lectures discuss real-world challenges (globalization, energy, environment, and health) and contribute to discussions on the widening scope of PSE/CAPE versus the consolidation of the core topics of PSE/CAPE. - Highlights how the Process Systems Engineering/Computer-Aided Process Engineering community contributes to the sustainability of modern society - Presents findings and discussions from both the 12th Process Systems Engineering (PSE) and 25th European Society of Computer-Aided Process Engineering (ESCAPE) Events - Establishes the core products of Process Systems Engineering/Computer Aided Process Engineering - Defines the future challenges of the Process Systems Engineering/Computer Aided Process Engineering community |
| optimization under constraints: Quantitative Planning and Control Yuji Ijiri, Andrew B. Whinston, 2014-06-28 Quantitative Planning and Control: Essays in Honor of William Wager Cooper on the Occasion of His 65th Birthday features a collection of papers prepared by students and associates of William Wager Cooper to honor him on the occasion of his sixty-fifth birthday. The book centers on the theme of Quantitative Planning and Control, the theme to which much of Professor Cooper's research effort has been devoted. The theme covers diverse fields of inquiry as reflected in the articles in this book, which are organized in four parts: (1) mathematical programming and decision models; (2) economic development and firm growth; (3) manpower planning and design; and (4) accounting and control. At the core of all of the articles in this book lies a belief that analytical approaches can help solve all managerial problems, a philosophy that is deeply rooted in Professor Cooper's thinking. This book demonstrates how this fundamental view on management can be reflected in dealing with problems in various fields of management. In particular, the book focuses on three main areas of application of this view, economic development, manpower planning, and accounting and control, along with the subject of developing tools that are necessary for solving managerial problems analytically. |
| optimization under constraints: Handbook of Constraint Programming Francesca Rossi, Peter Van Beek, Toby Walsh, 2006 Of course each line of work is dealt with in a survey-like style, where some details may be neglected in favor of coverage. However, the extensive bibliography of each chapter will help the interested readers to find suitable sources for the missing details. Each chapter of the handbook is intended to be a self-contained survey of a topic, and is written by one or more authors who are leading researchers in the area. The intended audience of the handbook is researchers, graduate students, higher-year undergraduates and practitioners who wish to learn about the state-of-the-art in constraint programming. No prior knowledge about the field is necessary to be able to read the chapters and gather useful knowledge.- |
| optimization under constraints: Advances and Trends in Optimization with Engineering Applications Tamas Terlaky, Miguel F. Anjos, Shabbir Ahmed, 2017-04-26 Optimization is of critical importance in engineering. Engineers constantly strive for the best possible solutions, the most economical use of limited resources, and the greatest efficiency. As system complexity increases, these goals mandate the use of state-of-the-art optimization techniques. In recent years, the theory and methodology of optimization have seen revolutionary improvements. Moreover, the exponential growth in computational power, along with the availability of multicore computing with virtually unlimited memory and storage capacity, has fundamentally changed what engineers can do to optimize their designs. This is a two-way process: engineers benefit from developments in optimization methodology, and challenging new classes of optimization problems arise from novel engineering applications. Advances and Trends in Optimization with Engineering Applications reviews 10 major areas of optimization and related engineering applications, providing a broad summary of state-of-the-art optimization techniques most important to engineering practice. Each part provides a clear overview of a specific area and discusses a range of real-world problems. The book provides a solid foundation for engineers and mathematical optimizers alike who want to understand the importance of optimization methods to engineering and the capabilities of these methods. |
| optimization under constraints: Applications of Mathematics in Economics Warren Page, 2013 Shows instructors what mathematics is used at the undergraduate level in various parts of economics. Separate sections provide students with opportunities to apply their mathematics in relevant economics contexts. Brings together many different mathematics applications to such varied economics topics. |
| optimization under constraints: Nonlinear Optimization William P. Fox, 2020-12-08 Optimization is the act of obtaining the best result under given circumstances. In design, construction, and maintenance of any engineering system, engineers must make technological and managerial decisions to minimize either the effort or cost required or to maximize benefits. There is no single method available for solving all optimization problems efficiently. Several optimization methods have been developed for different types of problems. The optimum-seeking methods are mathematical programming techniques (specifically, nonlinear programming techniques). Nonlinear Optimization: Models and Applications presents the concepts in several ways to foster understanding. Geometric interpretation: is used to re-enforce the concepts and to foster understanding of the mathematical procedures. The student sees that many problems can be analyzed, and approximate solutions found before analytical solutions techniques are applied. Numerical approximations: early on, the student is exposed to numerical techniques. These numerical procedures are algorithmic and iterative. Worksheets are provided in Excel, MATLAB®, and MapleTM to facilitate the procedure. Algorithms: all algorithms are provided with a step-by-step format. Examples follow the summary to illustrate its use and application. Nonlinear Optimization: Models and Applications: Emphasizes process and interpretation throughout Presents a general classification of optimization problems Addresses situations that lead to models illustrating many types of optimization problems Emphasizes model formulations Addresses a special class of problems that can be solved using only elementary calculus Emphasizes model solution and model sensitivity analysis About the author: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. He received his Ph.D. at Clemson University and has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics. He has written many publications, including over 20 books and over 150 journal articles. Currently, he is an adjunct professor in the Department of Mathematics at the College of William and Mary. He is the emeritus director of both the High School Mathematical Contest in Modeling and the Mathematical Contest in Modeling. |
| optimization under constraints: Advances in Optimization and Numerical Analysis S. Gomez, J.P. Hennart, 1994-04-30 In January 1992, the Sixth Workshop on Optimization and Numerical Analysis was held in the heart of the Mixteco-Zapoteca region, in the city of Oaxaca, Mexico, a beautiful and culturally rich site in ancient, colonial and modern Mexican civiliza tion. The Workshop was organized by the Numerical Analysis Department at the Institute of Research in Applied Mathematics of the National University of Mexico in collaboration with the Mathematical Sciences Department at Rice University, as were the previous ones in 1978, 1979, 1981, 1984 and 1989. As were the third, fourth, and fifth workshops, this one was supported by a grant from the Mexican National Council for Science and Technology, and the US National Science Foundation, as part of the joint Scientific and Technical Cooperation Program existing between these two countries. The participation of many of the leading figures in the field resulted in a good representation of the state of the art in Continuous Optimization, and in an over view of several topics including Numerical Methods for Diffusion-Advection PDE problems as well as some Numerical Linear Algebraic Methods to solve related pro blems. This book collects some of the papers given at this Workshop. |
Mathematical optimization - Wikipedia
High-level controllers such as model predictive control (MPC) or real-time optimization (RTO) employ mathematical optimization. These algorithms run online and repeatedly determine …
Optimization | Definition, Techniques, & Facts | Britannica
Optimization, collection of mathematical principles and methods used for solving quantitative problems. Optimization problems typically have three fundamental elements: a quantity to be …
OPTIMIZATION Definition & Meaning - Merriam-Webster
The meaning of OPTIMIZATION is an act, process, or methodology of making something (such as a design, system, or decision) as fully perfect, functional, or effective as possible; specifically : …
Optimization - Taylor & Francis Online
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1. WHAT IS OPTIMIZATION? - University of Washington
1. WHAT IS OPTIMIZATION? Optimization problem: Maximizing or minimizing some function relative to some set, often representing a range of choices available in a certain situation. The …
Calculus I - Optimization - Pauls Online Math Notes
Nov 16, 2022 · In optimization problems we are looking for the largest value or the smallest value that a function can take. We saw how to solve one kind of optimization problem in the Absolute …
OPTIMIZATION | English meaning - Cambridge Dictionary
OPTIMIZATION definition: 1. the act of making something as good as possible: 2. the act of making something as good as…. Learn more.
Introduction to Mathematical Optimization - Stanford University
Mathematical Optimization in the “Real World” Mathematical Optimization is a branch of applied mathematics which is useful in many different fields. Here are a few examples: •Manufacturing …
A Brief Overview of Optimization Problems - MIT …
Why optimization? • In some sense, all engineering design . is optimization: choosing design parameters to improve some objective • Much of . data analysis . is also optimization: …
Optimization for Data Science - GeeksforGeeks
Jul 25, 2024 · What's Optimization? Wikipedia defines optimization as a problem where you maximize or minimize a real function by systematically choosing input values from an allowed …
Mathematical optimization - Wikip…
High-level controllers such as model predictive control (MPC) or real-time optimization (RTO) employ mathematical optimization. …
Optimization | Definition, Technique…
Optimization, collection of mathematical principles and methods used for solving quantitative problems. Optimization problems …
OPTIMIZATION Definition & Meaning …
The meaning of OPTIMIZATION is an act, process, or methodology of making something (such as a design, system, or …
Optimization - Taylor & Francis Online
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1. WHAT IS OPTIMIZATION?
1. WHAT IS OPTIMIZATION? Optimization problem: Maximizing or minimizing some function relative to some set, often …
