Download or read book Duality in Nonlinear Vector Optimization written by Wing Wah Loh and published by . This book was released on 1989 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Generalized Convexity and Vector Optimization written by Shashi K. Mishra and published by Springer Science & Business Media. This book was released on 2008-12-19 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present lecture note is dedicated to the study of the optimality conditions and the duality results for nonlinear vector optimization problems, in ?nite and in?nite dimensions. The problems include are nonlinear vector optimization problems, s- metric dual problems, continuous-time vector optimization problems, relationships between vector optimization and variational inequality problems. Nonlinear vector optimization problems arise in several contexts such as in the building and interpretation of economic models; the study of various technolo- cal processes; the development of optimal choices in ?nance; management science; production processes; transportation problems and statistical decisions, etc. In preparing this lecture note a special effort has been made to obtain a se- contained treatment of the subjects; so we hope that this may be a suitable source for a beginner in this fast growing area of research, a semester graduate course in nonlinear programing, and a good reference book. This book may be useful to theoretical economists, engineers, and applied researchers involved in this area of active research. The lecture note is divided into eight chapters: Chapter 1 brie?y deals with the notion of nonlinear programing problems with basic notations and preliminaries. Chapter 2 deals with various concepts of convex sets, convex functions, invex set, invex functions, quasiinvex functions, pseudoinvex functions, type I and generalized type I functions, V-invex functions, and univex functions.

Download or read book Duality in Vector Optimization written by Radu Ioan Bot and published by Springer Science & Business Media. This book was released on 2009-08-12 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. One chapter is exclusively consecrated to the scalar and vector Wolfe and Mond-Weir duality schemes.

Download or read book Duality in Optimization and Variational Inequalities written by C.j. Goh and published by Taylor & Francis. This book was released on 2002-05-10 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimization and Variational Inequalities is intended for researchers and practitioners of optimization with the aim of enhancing their understanding of duality. It provides a wider appreciation of optimality conditions in various scenarios and under different assumptions. It will enable the reader to use duality to devise more effective computational methods, and to aid more meaningful interpretation of optimization and variational inequality problems.

Download or read book Conjugate Duality and Optimization written by R. Tyrrell Rockafellar and published by SIAM. This book was released on 1974-01-01 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. An emphasis is placed on the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.

Download or read book Optimality Conditions in Vector Optimization written by Manuel Arana Jiménez and published by Bentham Science Publishers. This book was released on 2010 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector optimization is continuously needed in several science fields, particularly in economy, business, engineering, physics and mathematics. The evolution of these fields depends, in part, on the improvements in vector optimization in mathematical programming. The aim of this Ebook is to present the latest developments in vector optimization. The contributions have been written by some of the most eminent researchers in this field of mathematical programming. The Ebook is considered essential for researchers and students in this field.

Download or read book Linear and Nonlinear Optimization written by Igor Griva and published by SIAM. This book was released on 2009-01-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to the applications, theory, and algorithms of linear and nonlinear optimization. The emphasis is on practical aspects - discussing modern algorithms, as well as the influence of theory on the interpretation of solutions or on the design of software. The book includes several examples of realistic optimization models that address important applications. The succinct style of this second edition is punctuated with numerous real-life examples and exercises, and the authors include accessible explanations of topics that are not often mentioned in textbooks, such as duality in nonlinear optimization, primal-dual methods for nonlinear optimization, filter methods, and applications such as support-vector machines. The book is designed to be flexible. It has a modular structure, and uses consistent notation and terminology throughout. It can be used in many different ways, in many different courses, and at many different levels of sophistication.

Download or read book Introduction to the Theory of Nonlinear Optimization written by Johannes Jahn and published by Springer Nature. This book was released on 2020-07-02 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.

Download or read book V Invex Functions and Vector Optimization written by Shashi K. Mishra and published by Springer Science & Business Media. This book was released on 2007-11-17 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume summarizes and synthesizes an aspect of research work that has been done in the area of Generalized Convexity over the past few decades. Specifically, the book focuses on V-invex functions in vector optimization that have grown out of the work of Jeyakumar and Mond in the 1990’s. The authors integrate related research into the book and demonstrate the wide context from which the area has grown and continues to grow.

Download or read book Theory of Vector Optimization written by Dinh The Luc and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes grew out of a series of lectures given by the author at the Univer sity of Budapest during 1985-1986. Additional results have been included which were obtained while the author was at the University of Erlangen-Niirnberg under a grant of the Alexander von Humboldt Foundation. Vector optimization has two main sources coming from economic equilibrium and welfare theories of Edgeworth (1881) and Pareto (1906) and from mathemat ical backgrounds of ordered spaces of Cantor (1897) and Hausdorff (1906). Later, game theory of Borel (1921) and von Neumann (1926) and production theory of Koopmans (1951) have also contributed to this area. However, only in the fifties, after the publication of Kuhn-Tucker's paper (1951) on the necessary and sufficient conditions for efficiency, and of Deubreu's paper (1954) on valuation equilibrium and Pareto optimum, has vector optimization been recognized as a mathematical discipline. The stretching development of this field began later in the seventies and eighties. Today there are a number of books on vector optimization. Most of them are concerned with the methodology and the applications. Few of them offer a systematic study of the theoretical aspects. The aim of these notes is to pro vide a unified background of vector optimization,with the emphasis on nonconvex problems in infinite dimensional spaces ordered by convex cones. The notes are arranged into six chapters. The first chapter presents prelim inary material.

Download or read book Linear and Nonlinear Optimization written by Richard W. Cottle and published by Springer. This book was released on 2017-06-11 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​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

Download or read book Vector Optimization written by Guang-ya Chen and published by Springer Science & Business Media. This book was released on 2005-07-13 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to vector or multiple criteria approaches in optimization. Topics covered include: vector optimization, vector variational inequalities, vector variational principles, vector minmax inequalities and vector equilibrium problems. In particular, problems with variable ordering relations and set-valued mappings are treated. The nonlinear scalarization method is extensively used throughout the book to deal with various vector-related problems. The results presented are original and should be interesting to researchers and graduates in applied mathematics and operations research. Readers will benefit from new methods and ideas for handling multiple criteria decision problems.

Download or read book Vector Optimization written by Johannes Jahn and published by Springer Science & Business Media. This book was released on 2013-06-05 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: In vector optimization one investigates optimal elements such as min imal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space. The prob lem of determining at least one of these optimal elements, if they exist at all, is also called a vector optimization problem. Problems of this type can be found not only in mathematics but also in engineer ing and economics. Vector optimization problems arise, for exam ple, in functional analysis (the Hahn-Banach theorem, the lemma of Bishop-Phelps, Ekeland's variational principle), multiobjective pro gramming, multi-criteria decision making, statistics (Bayes solutions, theory of tests, minimal covariance matrices), approximation theory (location theory, simultaneous approximation, solution of boundary value problems) and cooperative game theory (cooperative n player differential games and, as a special case, optimal control problems). In the last decade vector optimization has been extended to problems with set-valued maps. This new field of research, called set optimiza tion, seems to have important applications to variational inequalities and optimization problems with multivalued data. The roots of vector optimization go back to F. Y. Edgeworth (1881) and V. Pareto (1896) who has already given the definition of the standard optimality concept in multiobjective optimization. But in mathematics this branch of optimization has started with the leg endary paper of H. W. Kuhn and A. W. Tucker (1951). Since about v Vl Preface the end of the 60's research is intensively made in vector optimization.

Download or read book Nonlinear Optimization written by Andrzej Ruszczynski and published by Princeton University Press. This book was released on 2011-09-19 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems. Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.

Download or read book Optimization by Vector Space Methods written by David G. Luenberger and published by John Wiley & Sons. This book was released on 1997-01-23 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.

Download or read book Continuous Optimization and Variational Inequalities written by Anurag Jayswal and published by CRC Press. This book was released on 2022-09-13 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proposed book provides a comprehensive coverage of theory and methods in the areas of continuous optimization and variational inequality. It describes theory and solution methods for optimization with smooth and non-smooth functions, for variational inequalities with single-valued and multivalued mappings, and for related classes such as mixed variational inequalities, complementarity problems, and general equilibrium problems. The emphasis is made on revealing generic properties of these problems that allow creation of efficient solution methods. Salient Features The book presents a deep, wide-ranging introduction to the theory of the optimal control of processes governed by optimization techniques and variational inequality Several solution methods are provided which will help the reader to develop various optimization tools for real-life problems which can be modeled by optimization techniques involving linear and nonlinear functions. The book focuses on most recent contributions in the nonlinear phenomena, which can appear in various areas of human activities. This book also presents relevant mathematics clearly and simply to help solve real life problems in diverse fields such as mechanical engineering, management, control behavior, traffic signal, industry, etc. This book is aimed primarily at advanced undergraduates and graduate students pursuing computer engineering and electrical engineering courses. Researchers, academicians and industry people will also find this book useful.

Download or read book Duality Principles in Nonconvex Systems written by David Yang Gao and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.