Trust Region Methods

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Publisher : SIAM
ISBN 13 : 0898714605
Total Pages : 960 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Trust Region Methods by : A. R. Conn

Download or read book Trust Region Methods written by A. R. Conn and published by SIAM. This book was released on 2000-01-01 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Implementation of Trust Region Methods in Optimization

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Publisher :
ISBN 13 :
Total Pages : 88 pages
Book Rating : 4.:/5 (92 download)

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Book Synopsis Implementation of Trust Region Methods in Optimization by : Mohammed Omar Hajj

Download or read book Implementation of Trust Region Methods in Optimization written by Mohammed Omar Hajj and published by . This book was released on 1998 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Programming The State of the Art

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Publisher : Springer Science & Business Media
ISBN 13 : 3642688748
Total Pages : 662 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Mathematical Programming The State of the Art by : A. Bachem

Download or read book Mathematical Programming The State of the Art written by A. Bachem and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the late forties, Mathematical Programming became a scientific discipline in its own right. Since then it has experienced a tremendous growth. Beginning with economic and military applications, it is now among the most important fields of applied mathematics with extensive use in engineering, natural sciences, economics, and biological sciences. The lively activity in this area is demonstrated by the fact that as early as 1949 the first "Symposium on Mathe matical Programming" took place in Chicago. Since then mathematical programmers from all over the world have gath ered at the intfrnational symposia of the Mathematical Programming Society roughly every three years to present their recent research, to exchange ideas with their colleagues and to learn about the latest developments in their own and related fields. In 1982, the XI. International Symposium on Mathematical Programming was held at the University of Bonn, W. Germany, from August 23 to 27. It was organized by the Institut fUr Okonometrie und Operations Re search of the University of Bonn in collaboration with the Sonderforschungs bereich 21 of the Deutsche Forschungsgemeinschaft. This volume constitutes part of the outgrowth of this symposium and docu ments its scientific activities. Part I of the book contains information about the symposium, welcoming addresses, lists of committees and sponsors and a brief review about the Ful kerson Prize and the Dantzig Prize which were awarded during the opening ceremony.

Introduction to Derivative-Free Optimization

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Publisher : SIAM
ISBN 13 : 0898716683
Total Pages : 276 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Introduction to Derivative-Free Optimization by : Andrew R. Conn

Download or read book Introduction to Derivative-Free Optimization written by Andrew R. Conn and published by SIAM. This book was released on 2009-04-16 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first contemporary comprehensive treatment of optimization without derivatives. This text explains how sampling and model techniques are used in derivative-free methods and how they are designed to solve optimization problems. It is designed to be readily accessible to both researchers and those with a modest background in computational mathematics.

Numerical Optimization

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Publisher : Springer Science & Business Media
ISBN 13 : 0387400656
Total Pages : 686 pages
Book Rating : 4.3/5 (874 download)

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Book Synopsis Numerical Optimization by : Jorge Nocedal

Download or read book Numerical Optimization written by Jorge Nocedal and published by Springer Science & Business Media. This book was released on 2006-12-11 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

Large-Scale Trust-Region Methods and Their Application to Primal-Dual Interior-Point Methods

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)

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Book Synopsis Large-Scale Trust-Region Methods and Their Application to Primal-Dual Interior-Point Methods by : Alexander Guldemond

Download or read book Large-Scale Trust-Region Methods and Their Application to Primal-Dual Interior-Point Methods written by Alexander Guldemond and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trust-region methods are amongst the most commonly used methods in unconstrained mathematical optimization. Their impressive performance and sound theoretical guarantees make them suitable for a wide range of problem types. However, the computational complexity of existing methods for solving the trust-region subproblem prevents trust-region methods from being widely used in large-scale problems in both unconstrained and constrained settings. This dissertation introduces and analyzes three novel methods for solving the trust-region subproblem for large-scale constrained optimization problems. Convergence rates and proofs are presented where applicable. Furthermore, a trust-region approach is developed for the recently introduced all-shifted primal-dual penalty-barrier method for solving nonconvex, constrained optimization problems. The three trust-region algorithms introduced are the shifted and inverted generalized Lanczos trust region algorithm, the locally optimal preconditioned conjugate gradient trust region, and the Jacobi-Davidson QZ trust region algorithm. Each new method exhibits improved performance over the existing standard methods and is best suited for problems too large for the traditional methods to handle efficiently. Furthermore, each method exhibits particular benefits for differently scaled problems.

Algorithms for Decision Making

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Publisher : MIT Press
ISBN 13 : 0262047012
Total Pages : 701 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Algorithms for Decision Making by : Mykel J. Kochenderfer

Download or read book Algorithms for Decision Making written by Mykel J. Kochenderfer and published by MIT Press. This book was released on 2022-08-16 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: A broad introduction to algorithms for decision making under uncertainty, introducing the underlying mathematical problem formulations and the algorithms for solving them. Automated decision-making systems or decision-support systems—used in applications that range from aircraft collision avoidance to breast cancer screening—must be designed to account for various sources of uncertainty while carefully balancing multiple objectives. This textbook provides a broad introduction to algorithms for decision making under uncertainty, covering the underlying mathematical problem formulations and the algorithms for solving them. The book first addresses the problem of reasoning about uncertainty and objectives in simple decisions at a single point in time, and then turns to sequential decision problems in stochastic environments where the outcomes of our actions are uncertain. It goes on to address model uncertainty, when we do not start with a known model and must learn how to act through interaction with the environment; state uncertainty, in which we do not know the current state of the environment due to imperfect perceptual information; and decision contexts involving multiple agents. The book focuses primarily on planning and reinforcement learning, although some of the techniques presented draw on elements of supervised learning and optimization. Algorithms are implemented in the Julia programming language. Figures, examples, and exercises convey the intuition behind the various approaches presented.

Real-Time Optimization

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Publisher : MDPI
ISBN 13 : 303842448X
Total Pages : 255 pages
Book Rating : 4.0/5 (384 download)

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Book Synopsis Real-Time Optimization by : Dominique Bonvin

Download or read book Real-Time Optimization written by Dominique Bonvin and published by MDPI. This book was released on 2018-07-05 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Real-Time Optimization" that was published in Processes

Frontiers in PDE-Constrained Optimization

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Publisher : Springer
ISBN 13 : 1493986368
Total Pages : 434 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Frontiers in PDE-Constrained Optimization by : Harbir Antil

Download or read book Frontiers in PDE-Constrained Optimization written by Harbir Antil and published by Springer. This book was released on 2018-10-12 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications. Many science and engineering applications necessitate the solution of optimization problems constrained by physical laws that are described by systems of partial differential equations (PDEs)​. As a result, PDE-constrained optimization problems arise in a variety of disciplines including geophysics, earth and climate science, material science, chemical and mechanical engineering, medical imaging and physics. This volume is divided into two parts. The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. Special emphasis is placed on algorithm development and numerical computation. In addition, a comprehensive treatment of inverse problems arising in the oil and gas industry is provided. The second part of this volume focuses on the application of PDE-constrained optimization, including problems in optimal control, optimal design, and inverse problems, among other topics.

Mixed Integer Nonlinear Programming

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Publisher : Springer Science & Business Media
ISBN 13 : 1461419271
Total Pages : 687 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Mixed Integer Nonlinear Programming by : Jon Lee

Download or read book Mixed Integer Nonlinear Programming written by Jon Lee and published by Springer Science & Business Media. This book was released on 2011-12-02 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances.

Algorithms for Optimization

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Publisher : MIT Press
ISBN 13 : 0262039427
Total Pages : 521 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Algorithms for Optimization by : Mykel J. Kochenderfer

Download or read book Algorithms for Optimization written by Mykel J. Kochenderfer and published by MIT Press. This book was released on 2019-03-12 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Constrained Markov Decision Processes

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Publisher : Routledge
ISBN 13 : 1351458248
Total Pages : 256 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Constrained Markov Decision Processes by : Eitan Altman

Download or read book Constrained Markov Decision Processes written by Eitan Altman and published by Routledge. This book was released on 2021-12-17 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified approach for the study of constrained Markov decision processes with a finite state space and unbounded costs. Unlike the single controller case considered in many other books, the author considers a single controller with several objectives, such as minimizing delays and loss, probabilities, and maximization of throughputs. It is desirable to design a controller that minimizes one cost objective, subject to inequality constraints on other cost objectives. This framework describes dynamic decision problems arising frequently in many engineering fields. A thorough overview of these applications is presented in the introduction. The book is then divided into three sections that build upon each other.

Trust-region Methods for Simulation Based Nonlinear Optimization

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Publisher :
ISBN 13 : 9783844001853
Total Pages : 262 pages
Book Rating : 4.0/5 (18 download)

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Book Synopsis Trust-region Methods for Simulation Based Nonlinear Optimization by : Alexander Thekale

Download or read book Trust-region Methods for Simulation Based Nonlinear Optimization written by Alexander Thekale and published by . This book was released on 2011 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Engineering Design Optimization

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Publisher : Cambridge University Press
ISBN 13 : 110898861X
Total Pages : 653 pages
Book Rating : 4.1/5 (89 download)

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Book Synopsis Engineering Design Optimization by : Joaquim R. R. A. Martins

Download or read book Engineering Design Optimization written by Joaquim R. R. A. Martins and published by Cambridge University Press. This book was released on 2021-11-18 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Theory of Optimization

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Publisher : Springer Science & Business Media
ISBN 13 : 1475757956
Total Pages : 277 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Mathematical Theory of Optimization by : Ding-Zhu Du

Download or read book Mathematical Theory of Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical theory of optimization. It emphasizes the convergence theory of nonlinear optimization algorithms and applications of nonlinear optimization to combinatorial optimization. Mathematical Theory of Optimization includes recent developments in global convergence, the Powell conjecture, semidefinite programming, and relaxation techniques for designs of approximation solutions of combinatorial optimization problems.

Derivative-Free and Blackbox Optimization

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Publisher : Springer
ISBN 13 : 3319689134
Total Pages : 307 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Derivative-Free and Blackbox Optimization by : Charles Audet

Download or read book Derivative-Free and Blackbox Optimization written by Charles Audet and published by Springer. This book was released on 2017-12-02 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed as a textbook, suitable for self-learning or for teaching an upper-year university course on derivative-free and blackbox optimization. The book is split into 5 parts and is designed to be modular; any individual part depends only on the material in Part I. Part I of the book discusses what is meant by Derivative-Free and Blackbox Optimization, provides background material, and early basics while Part II focuses on heuristic methods (Genetic Algorithms and Nelder-Mead). Part III presents direct search methods (Generalized Pattern Search and Mesh Adaptive Direct Search) and Part IV focuses on model-based methods (Simplex Gradient and Trust Region). Part V discusses dealing with constraints, using surrogates, and bi-objective optimization. End of chapter exercises are included throughout as well as 15 end of chapter projects and over 40 figures. Benchmarking techniques are also presented in the appendix.

Extremum-Seeking Control and Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 1447122240
Total Pages : 210 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Extremum-Seeking Control and Applications by : Chunlei Zhang

Download or read book Extremum-Seeking Control and Applications written by Chunlei Zhang and published by Springer Science & Business Media. This book was released on 2011-10-26 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extremum-seeking control tracks a varying maximum or minimum in a performance function such as output or cost. It attempts to determine the optimal performance of a control system as it operates, thereby reducing downtime and the need for system analysis. Extremum-seeking Control and Applications is divided into two parts. In the first, the authors review existing analog-optimization-based extremum-seeking control including gradient-, perturbation- and sliding-mode-based control designs. They then propose a novel numerical-optimization-based extremum-seeking control based on optimization algorithms and state regulation. This control design is developed for simple linear time-invariant systems and then extended for a class of feedback linearizable nonlinear systems. The two main optimization algorithms – line search and trust region methods – are analyzed for robustness. Finite-time and asymptotic state regulators are put forward for linear and nonlinear systems respectively. Further design flexibility is achieved using the robustness results of the optimization algorithms and the asymptotic state regulator by which existing nonlinear adaptive control techniques can be introduced for robust design. The approach used is easier to implement and tends to be more robust than those that use perturbation-based extremum-seeking control. The second part of the book deals with a variety of applications of extremum-seeking control: a comparative study of extremum-seeking control schemes in antilock braking system design; source seeking, formation control, collision and obstacle avoidance for groups of autonomous agents; mobile radar networks; and impedance matching. MATLAB®/Simulink® code which can be downloaded from www.springer.com/ISBN helps readers to reproduce the results presented in the text and gives them a head start for implementing the algorithms in their own applications. Extremum-seeking Control and Applications will interest academics and graduate students working in control, and industrial practitioners from a variety of backgrounds: systems, automotive, aerospace, communications, semiconductor and chemical engineering.