Author: Richard W. Cottle Publisher: Springer ISBN: 1493970550 Category : Business & Economics Languages : en Pages : 644
Book Description
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: Yurii Nesterov Publisher: SIAM ISBN: 9781611970791 Category : Mathematics Languages : en Pages : 414
Book Description
Specialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. A background in linear algebra and mathematical programming is necessary to understand the book. The detailed proofs and lack of "numerical examples" might suggest that the book is of limited value to the reader interested in the practical aspects of convex optimization, but nothing could be further from the truth. An entire chapter is devoted to potential reduction methods precisely because of their great efficiency in practice.
Author: Lorenz T. Biegler Publisher: SIAM ISBN: 0898719380 Category : Science Languages : en Pages : 411
Book Description
This book addresses modern nonlinear programming (NLP) concepts and algorithms, especially as they apply to challenging applications in chemical process engineering. The author provides a firm grounding in fundamental NLP properties and algorithms, and relates them to real-world problem classes in process optimization, thus making the material understandable and useful to chemical engineers and experts in mathematical optimization.
Author: A. Iserles Publisher: Cambridge University Press ISBN: 9780521516426 Category : Mathematics Languages : en Pages : 424
Book Description
A high-impact, prestigious annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.
Author: Françoise Lamnabhi-Lagarrigu Publisher: John Wiley & Sons ISBN: 1118615131 Category : Technology & Engineering Languages : en Pages : 605
Book Description
This book gathers together a selection of papers presented at the Joint CTS-HYCON Workshop on Nonlinear and Hybrid Control held at the Paris Sorbonne, France, 10-12 July 2006. The main objective of the Workshop was to promote the exchange of ideas and experiences and reinforce scientific contacts in the large multidisciplinary area of the control of nonlinear and hybrid systems.
Author: Panos M. Pardalos and Henry Wolkowicz Publisher: American Mathematical Soc. ISBN: 9780821871256 Category : Interior-point methods Languages : en Pages : 276
Book Description
This volume presents refereed papers presented at the workshop Semidefinite Programming and Interior-Point Approaches for Combinatorial Problems: held at The Fields Institute in May 1996. Semidefinite programming (SDP) is a generalization of linear programming (LP) in that the non-negativity constraints on the variables is replaced by a positive semidefinite constraint on matrix variables. Many of the elegant theoretical properties and powerful solution techniques follow through from LP to SDP. In particular, the primal-dual interior-point methods, which are currently so successful for LP, can be used to efficiently solve SDP problems. In addition to the theoretical and algorithmic questions, SDP has found many important applications in combinatorial optimization, control theory and other areas of mathematical programming. The papers in this volume cover a wide spectrum of recent developments in SDP. The volume would be suitable as a textbook for advanced courses in optimization. It is intended for graduate students and researchers in mathematics, computer science, engineering and operations.
Author: Stephen P. Boyd Publisher: Cambridge University Press ISBN: 9780521833783 Category : Business & Economics Languages : en Pages : 744
Book Description
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Author: Cornelis Roos Publisher: Springer Science & Business Media ISBN: 0387263799 Category : Mathematics Languages : en Pages : 501
Book Description
The era of interior point methods (IPMs) was initiated by N. Karmarkar’s 1984 paper, which triggered turbulent research and reshaped almost all areas of optimization theory and computational practice. This book offers comprehensive coverage of IPMs. It details the main results of more than a decade of IPM research. Numerous exercises are provided to aid in understanding the material.
Author: David G. Luenberger Publisher: Springer Nature ISBN: 3030854507 Category : Business & Economics Languages : en Pages : 609
Book Description
The 5th edition of this classic textbook covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve that problem. End-of-chapter exercises are provided for all chapters. The material is organized into three separate parts. Part I offers a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. In turn, Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. As such, Parts II and III can easily be used without reading Part I and, in fact, the book has been used in this way at many universities. New to this edition are popular topics in data science and machine learning, such as the Markov Decision Process, Farkas’ lemma, convergence speed analysis, duality theories and applications, various first-order methods, stochastic gradient method, mirror-descent method, Frank-Wolf method, ALM/ADMM method, interior trust-region method for non-convex optimization, distributionally robust optimization, online linear programming, semidefinite programming for sensor-network localization, and infeasibility detection for nonlinear optimization.
Author: Richard W. Cottle
Author: Yurii Nesterov
Author: Lorenz T. Biegler
Author: A. Iserles
Author: Françoise Lamnabhi-Lagarrigu
Author: Panos M. Pardalos and Henry Wolkowicz
Author: 
Author: Stephen P. Boyd
Author: Cornelis Roos
Author: David G. Luenberger