Algorithms For Nonlinearly Constrained Optimization

Author : Michael Thomas Heath,Stanford University. Computer Science Department
Publisher : Unknown
Page : 312 pages
File Size : 40,6 Mb
Release : 1978
Category : Algorithms
ISBN : STANFORD:36105031966992

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Numerical Algorithms for Nonlinearly Constrained Optimization by Michael Thomas Heath,Stanford University. Computer Science Department Pdf

This dissertation is concerned with the development and numerical implementation of algorithms for solving finite dimensional optimization problems. Special emphasis is given to robustness, by which is meant the ability of an algorithm to cope with adverse circumstances, whether due to pathologies of a particular problem or to the shortcomings of finite precision computer arithmetic. A uniform framework is developed in which a common set of techniques may be applied to all of the standard problems of optimization. The algorithms are based on Newton-like methods implemented in a robust manner by means of hybrid, curved line searches and stable linear algebra techniques. Developed first in the context of systems of nonlinear equations, nonlinear least squares, and unconstrained minimization, the algorithms are combined and extended to include problems with equality or inequality constraints. Constrained problems are handled by means of separate line searches in the range and null spaces of the matrix of constraint normals. The classical Lagrangian is modified to allow the same Newton-like methods to be applied to inequality constraints. Test results are presented which show the validity and promise of the methods developed in this dissertation. (Author).

Author : Stanford University. Systems Optimization Laboratory
Publisher : Unknown
Page : 48 pages
File Size : 43,6 Mb
Release : 1979
Category : Electronic
ISBN : STANFORD:36105046361965

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Algorithms for Nonlinearly Constrained Optimization by Stanford University. Systems Optimization Laboratory Pdf

Author : Richard W. Cottle,Mukund N. Thapa
Publisher : Springer
Page : 614 pages
File Size : 49,7 Mb
Release : 2017-06-11
Category : Business & Economics
ISBN : 9781493970551

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Linear and Nonlinear Optimization by Richard W. Cottle,Mukund N. Thapa Pdf

​This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises. The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University. It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes. "This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details. This is an ideal book for teaching a one or two semester masters-level course in optimization – it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study." Professor Ilan Adler, IEOR Department, UC Berkeley "A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields." Michael P. Friedlander, IBM Professor of Computer Science, Professor of Mathematics, University of British Columbia

Author : Courant Institute of Mathematical Sciences. Computer Science Department
Publisher : Unknown
Page : 0 pages
File Size : 55,8 Mb
Release : 1983
Category : Electronic
ISBN : OCLC:123320524

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Projected Hessian Updating Algorithms for Nonlinearly Constrained Optimization by Courant Institute of Mathematical Sciences. Computer Science Department Pdf

Author : Gianni Pillo,Massimo Roma
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 47,5 Mb
Release : 2006-06-03
Category : Mathematics
ISBN : 9780387300658

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Large-Scale Nonlinear Optimization by Gianni Pillo,Massimo Roma Pdf

This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.

Author : Mokhtar S. Bazaraa,Hanif D. Sherali,C. M. Shetty
Publisher : John Wiley & Sons
Page : 867 pages
File Size : 40,5 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781118626306

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Nonlinear Programming by Mokhtar S. Bazaraa,Hanif D. Sherali,C. M. Shetty Pdf

COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED Nonlinear Programming: Theory and Algorithms—now in an extensively updated Third Edition—addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The Third Edition begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction. Concentration on the three major parts of nonlinear programming is provided: Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programming Optimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditions Algorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problems Important features of the Third Edition include: New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and more Updated discussion and new applications in each chapter Detailed numerical examples and graphical illustrations Essential coverage of modeling and formulating nonlinear programs Simple numerical problems Advanced theoretical exercises The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems.

Author : Ber? Rustem
Publisher : Wiley-Blackwell
Page : 328 pages
File Size : 50,7 Mb
Release : 1998-04-15
Category : Computers
ISBN : STANFORD:36105023173433

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Algorithms for Nonlinear Programming and Multiple-Objective Decisions by Ber? Rustem Pdf

Algorithms are solution methods used for optimal decision making in mathematics and operations research. This book is a study of algorithms for decision making with multiple objectives. It is a distillation of recent research in developing methodologies for solving optimal decision problems in economics, and engineering and reflects current research in these areas.

Author : Jorge Nocedal,Michael Overton
Publisher : Legare Street Press
Page : 0 pages
File Size : 54,9 Mb
Release : 2022-10-27
Category : History
ISBN : 1017473994

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Projected Hessian Updating Algorithms for Nonlinearly Constrained Optimization by Jorge Nocedal,Michael Overton Pdf

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : Jorge Nocedal
Publisher : Forgotten Books
Page : 78 pages
File Size : 45,8 Mb
Release : 2016-11-08
Category : Mathematics
ISBN : 1334213712

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Projected Hessian Updating Algorithms for Nonlinearly Constrained Optimization (Classic Reprint) by Jorge Nocedal Pdf

Excerpt from Projected Hessian Updating Algorithms for Nonlinearly Constrained Optimization Where f: irn IR 1 and c: R n R m are twice differentiable functions and m n. We will further assune that the Hessian matrices s and {vzci}, are Lipschitz continuous matrix functions of x. Although this problem arises frequently in many applications, a more common version involves inequality constraints. We confine our attention to partly because it is easier to address and partlv because a good understanding of algorithms for solving is essential for the design of methods for the more general problem. Note that we are concerned only with finding a local minimum of Finding the global minimum is a much more difficult task. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Amir Beck
Publisher : SIAM
Page : 282 pages
File Size : 44,6 Mb
Release : 2014-10-27
Category : Mathematics
ISBN : 9781611973655

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Introduction to Nonlinear Optimization by Amir Beck Pdf

This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization?theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems?and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes offers several subjects not typically found in optimization books?for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat?Weber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLAB? toolbox CVX and a package of m-files that is posted on the book?s web site.

Author : E. Spedicato
Publisher : Springer Science & Business Media
Page : 572 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400903692

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Algorithms for Continuous Optimization by E. Spedicato Pdf

The NATO Advanced Study Institute on "Algorithms for continuous optimiza tion: the state of the art" was held September 5-18, 1993, at II Ciocco, Barga, Italy. It was attended by 75 students (among them many well known specialists in optimiza tion) from the following countries: Belgium, Brasil, Canada, China, Czech Republic, France, Germany, Greece, Hungary, Italy, Poland, Portugal, Rumania, Spain, Turkey, UK, USA, Venezuela. The lectures were given by 17 well known specialists in the field, from Brasil, China, Germany, Italy, Portugal, Russia, Sweden, UK, USA. Solving continuous optimization problems is a fundamental task in computational mathematics for applications in areas of engineering, economics, chemistry, biology and so on. Most real problems are nonlinear and can be of quite large size. Devel oping efficient algorithms for continuous optimization has been an important field of research in the last 30 years, with much additional impetus provided in the last decade by the availability of very fast and parallel computers. Techniques, like the simplex method, that were already considered fully developed thirty years ago have been thoroughly revised and enormously improved. The aim of this ASI was to present the state of the art in this field. While not all important aspects could be covered in the fifty hours of lectures (for instance multiob jective optimization had to be skipped), we believe that most important topics were presented, many of them by scientists who greatly contributed to their development.

Author : Amir Beck
Publisher : SIAM
Page : 364 pages
File Size : 48,6 Mb
Release : 2023-06-29
Category : Mathematics
ISBN : 9781611977622

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Introduction to Nonlinear Optimization by Amir Beck Pdf

Built on the framework of the successful first edition, this book serves as a modern introduction to the field of optimization. The author’s objective is to provide the foundations of theory and algorithms of nonlinear optimization as well as to present a variety of applications from diverse areas of applied sciences. Introduction to Nonlinear Optimization gradually yet rigorously builds connections between theory, algorithms, applications, and actual implementation. The book contains several topics not typically included in optimization books, such as optimality conditions in sparsity constrained optimization, hidden convexity, and total least squares. Readers will discover a wide array of applications such as circle fitting, Chebyshev center, the Fermat–Weber problem, denoising, clustering, total least squares, and orthogonal regression. These applications are studied both theoretically and algorithmically, illustrating concepts such as duality. Python and MATLAB programs are used to show how the theory can be implemented. The extremely popular CVX toolbox (MATLAB) and CVXPY module (Python) are described and used. More than 250 theoretical, algorithmic, and numerical exercises enhance the reader's understanding of the topics. (More than 70 of the exercises provide detailed solutions, and many others are provided with final answers.) The theoretical and algorithmic topics are illustrated by Python and MATLAB examples. This book is intended for graduate or advanced undergraduate students in mathematics, computer science, electrical engineering, and potentially other engineering disciplines.

Author : Francisco J. Aragón,Miguel A. Goberna,Marco A. López,Margarita M.L. Rodríguez
Publisher : Springer
Page : 350 pages
File Size : 45,9 Mb
Release : 2019-02-27
Category : Mathematics
ISBN : 9783030111847

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Nonlinear Optimization by Francisco J. Aragón,Miguel A. Goberna,Marco A. López,Margarita M.L. Rodríguez Pdf

This textbook on nonlinear optimization focuses on model building, real world problems, and applications of optimization models to natural and social sciences. Organized into two parts, this book may be used as a primary text for courses on convex optimization and non-convex optimization. Definitions, proofs, and numerical methods are well illustrated and all chapters contain compelling exercises. The exercises emphasize fundamental theoretical results on optimality and duality theorems, numerical methods with or without constraints, and derivative-free optimization. Selected solutions are given. Applications to theoretical results and numerical methods are highlighted to help students comprehend methods and techniques.

Author : Ya-xiang Yuan
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 49,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461333357

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Advances in Nonlinear Programming by Ya-xiang Yuan Pdf

About 60 scientists and students attended the 96' International Conference on Nonlinear Programming, which was held September 2-5 at Institute of Compu tational Mathematics and Scientific/Engineering Computing (ICMSEC), Chi nese Academy of Sciences, Beijing, China. 25 participants were from outside China and 35 from China. The conference was to celebrate the 60's birthday of Professor M.J.D. Powell (Fellow of Royal Society, University of Cambridge) for his many contributions to nonlinear optimization. On behalf of the Chinese Academy of Sciences, vice president Professor Zhi hong Xu attended the opening ceremony of the conference to express his warm welcome to all the participants. After the opening ceremony, Professor M.J.D. Powell gave the keynote lecture "The use of band matrices for second derivative approximations in trust region methods". 13 other invited lectures on recent advances of nonlinear programming were given during the four day meeting: "Primal-dual methods for nonconvex optimization" by M. H. Wright (SIAM President, Bell Labs), "Interior point trajectories in semidefinite programming" by D. Goldfarb (Columbia University, Editor-in-Chief for Series A of Mathe matical Programming), "An approach to derivative free optimization" by A.

Author : Wenyu Sun,Ya-Xiang Yuan
Publisher : Springer Science & Business Media
Page : 689 pages
File Size : 50,8 Mb
Release : 2006-08-06
Category : Mathematics
ISBN : 9780387249766

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Optimization Theory and Methods by Wenyu Sun,Ya-Xiang Yuan Pdf

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.