Constrained Optimization and Lagrange Multiplier Methods

Author: Dimitri P. Bertsekas
Publisher: Academic Press
ISBN: 9781483260471
Release Date: 2014-05-10
Genre: Mathematics

Computer Science and Applied Mathematics: Constrained Optimization and Lagrange Multiplier Methods focuses on the advancements in the applications of the Lagrange multiplier methods for constrained minimization. The publication first offers information on the method of multipliers for equality constrained problems and the method of multipliers for inequality constrained and nondifferentiable optimization problems. Discussions focus on approximation procedures for nondifferentiable and ill-conditioned optimization problems; asymptotically exact minimization in the methods of multipliers; duality framework for the method of multipliers; and the quadratic penalty function method. The text then examines exact penalty methods, including nondifferentiable exact penalty functions; linearization algorithms based on nondifferentiable exact penalty functions; differentiable exact penalty functions; and local and global convergence of Lagrangian methods. The book ponders on the nonquadratic penalty functions of convex programming. Topics include large scale separable integer programming problems and the exponential method of multipliers; classes of penalty functions and corresponding methods of multipliers; and convergence analysis of multiplier methods. The text is a valuable reference for mathematicians and researchers interested in the Lagrange multiplier methods.

Linear Programming

Author: Vasek Chvatal
Publisher: Macmillan
ISBN: 0716715872
Release Date: 1983-09-15
Genre: Mathematics

For upper-division/graduate courses in operations research/management science, mathematics, and computer science, this text covers basic theory, selected applications, network flow problems, and advanced techniques.

Understanding and Using Linear Programming

Author: Jiri Matousek
Publisher: Springer Science & Business Media
ISBN: 9783540307174
Release Date: 2007-07-04
Genre: Mathematics

The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is "what every theoretical computer scientist should know about linear programming". A major focus is on applications of linear programming, both in practice and in theory. The book is concise, but at the same time, the main results are covered with complete proofs and in sufficient detail, ready for presentation in class. The book does not require more prerequisites than basic linear algebra, which is summarized in an appendix. One of its main goals is to help the reader to see linear programming "behind the scenes".

Theory of Linear and Integer Programming

Author: Alexander Schrijver
Publisher: John Wiley & Sons
ISBN: 0471982326
Release Date: 1998-07-07
Genre: Mathematics

Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the author's coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians. Contents 1 Introduction and preliminaries; 2 Problems, algorithms, and complexity; 3 Linear algebra and complexity; 4 Theory of lattices and linear diophantine equations; 5 Algorithms for linear diophantine equations; 6 Diophantine approximation and basis reduction; 7 Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; 8 The structure of polyhedra; 9 Polarity, and blocking and anti-blocking polyhedra; 10 Sizes and the theoretical complexity of linear inequalities and linear programming; 11 The simplex method; 12 Primal-dual, elimination, and relaxation methods; 13 Khachiyan's method for linear programming; 14 The ellipsoid method for polyhedra more generally; 15 Further polynomiality results in linear programming; 16 Introduction to integer linear programming; 17 Estimates in integer linear programming; 18 The complexity of integer linear programming; 19 Totally unimodular matrices: fundamental properties and examples; 20 Recognizing total unimodularity; 21 Further theory related to total unimodularity; 22 Integral polyhedra and total dual integrality; 23 Cutting planes; 24 Further methods in integer linear programming; Historical and further notes on integer linear programming; References; Notation index; Author index; Subject index

Linear Network Optimization

Author: Dimitri P. Bertsekas
Publisher: MIT Press
ISBN: 0262023342
Release Date: 1991
Genre: Business & Economics

Large-scale optimization is becoming increasingly important for students and professionals in electrical and industrial engineering, computer science, management science and operations research, and applied mathematics. Linear Network Optimization presents a thorough treatment of classical approaches to network problems such as shortest path, max-flow, assignment, transportation, and minimum cost flow problems. It is the first text to clearly explain important recent algorithms such as auction and relaxation, proposed by the author and others for the solution of these problems. Its coverage of both theory and implementations make it particularly useful as a text for a graduate-level course on network optimization as well as a practical guide to state-of-the-art codes in the field. Bertsekas focuses on the algorithms that have proved successful in practice and provides FORTRAN codes that implement them. The presentation is clear, mathematically rigorous, and economical. Many illustrations, examples, and exercises are included in the text. Dimitri P. Bertsekas is Professor of Electrical Engineering and Computer Science at MIT. Contents: Introduction. Simplex Methods. Dual Ascent Methods. Auction Algorithms. Performance and Comparisons. Appendixes.

Linear Programming

Author: Howard Karloff
Publisher: Springer Science & Business Media
ISBN: 9780817648435
Release Date: 2008-11-19
Genre: Computers

To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming.... Style is informal. ...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study. —Choice Reviews This is a textbook intended for advanced undergraduate or graduate students. It contains both theory and computational practice. —Zentralblatt Math

Introduction to Linear Optimization and Extensions with MATLAB

Author: Roy H. Kwon
Publisher: CRC Press
ISBN: 9781482204346
Release Date: 2013-09-05
Genre: Business & Economics

Filling the need for an introductory book on linear programming that discusses the important ways to mitigate parameter uncertainty, Introduction to Linear Optimization and Extensions with MATLAB® provides a concrete and intuitive yet rigorous introduction to modern linear optimization. In addition to fundamental topics, the book discusses current linear optimization technologies such as predictor-path following interior point methods for both linear and quadratic optimization as well as the inclusion of linear optimization of uncertainty i.e. stochastic programming with recourse and robust optimization. The author introduces both stochastic programming and robust optimization as frameworks to deal with parameter uncertainty. The author’s unusual approach—developing these topics in an introductory book—highlights their importance. Since most applications require decisions to be made in the face of uncertainty, the early introduction of these topics facilitates decision making in real world environments. The author also includes applications and case studies from finance and supply chain management that involve the use of MATLAB. Even though there are several LP texts in the marketplace, most do not cover data uncertainty using stochastic programming and robust optimization techniques. Most emphasize the use of MS Excel, while this book uses MATLAB which is the primary tool of many engineers, including financial engineers. The book focuses on state-of-the-art methods for dealing with parameter uncertainty in linear programming, rigorously developing theory and methods. But more importantly, the author’s meticulous attention to developing intuition before presenting theory makes the material come alive.

Author: Dimitri P. Bertsekas
Publisher: 清华大学出版社有限公司
ISBN: 7302123284
Release Date: 2006
Genre: Convex functions

国际知名大学原版教材信息技术学科与电气工程学科系列 30

INFORMS ABOK

Author: James J. Cochran
Publisher: Wiley
ISBN: 9781119483212
Release Date: 2018-10-23
Genre: Mathematics

Standardizes the definition and framework of analytics ABOK stands for Analytics Body of Knowledge. Based on the authors’ definition of analytics—which is “a process by which a team of people helps an organization make better decisions (the objective) through the analysis of data (the activity)”— this book from Institute for Operations Research and the Management Sciences (INFORMS) represents the perspectives of some of the most respected experts on analytics. The INFORMS ABOK documents the core concepts and skills with which an analytics professional should be familiar; establishes a dynamic resource that will be used by practitioners to increase their understanding of analytics; and, presents instructors with a framework for developing academic courses and programs in analytics. The INFORMS ABOK offers in-depth insight from peer-reviewed chapters that provide readers with a better understanding of the dynamic field of analytics. Chapters cover: Introduction to Analytics; Getting Started with Analytics; The Analytics Team; The Data; Solution Methodology; Model Building; Machine Learning; Deployment and Life Cycle Management; and The Blossoming Analytics Talent Pool: An Overview of the Analytics Ecosystem. Across industries and academia, readers with various backgrounds in analytics – from novices who are interested in learning more about the basics of analytics to experienced professionals who want a different perspective on some aspect of analytics – will benefit from reading about and implementing the concepts and methods covered by the INFORMS ABOK.

Nonlinear Programming

Author: Dimitri P. Bertsekas
Publisher:
ISBN: 1886529051
Release Date: 2016
Genre: Mathematical optimization

The third edition of the book is a thoroughly rewritten version of the 1999 2nd edition. New material was included, some of the old material was discarded, and a large portion of the remainder was reorganized or revised. This book provides a comprehensive and accessible presentation of algorithms for solving continuous optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. It places particular emphasis on modern developments, and their widespread applications in fields such as large-scale resource allocation problems, signal processing, and machine learning. The book was developed through instruction at MIT, focuses on nonlinear and other types of optimization: iterative algorithms for constrained and unconstrained optimization, Lagrange multipliers and duality, large scale problems, and the interface between continuous and discrete optimization. Among its special features, the book: 1) provides extensive coverage of iterative optimization methods within a unifying framework 2) provides a detailed treatment of interior point methods for linear programming 3) covers in depth duality theory from both a variational and a geometrical/convex analysis point of view 4) includes much new material on a number of topics, such as neural network training, large-scale optimization, signal processing, machine learning, and optimal control 5) includes a large number of examples and exercises detailed solutions of many of which are posted on the internet.

Optimization in Engineering

Author: Ramteen Sioshansi
Publisher: Springer
ISBN: 9783319567693
Release Date: 2017-06-24
Genre: Mathematics

This textbook covers the fundamentals of optimization, including linear, mixed-integer linear, nonlinear, and dynamic optimization techniques, with a clear engineering focus. It carefully describes classical optimization models and algorithms using an engineering problem-solving perspective, and emphasizes modeling issues using many real-world examples related to a variety of application areas. Providing an appropriate blend of practical applications and optimization theory makes the text useful to both practitioners and students, and gives the reader a good sense of the power of optimization and the potential difficulties in applying optimization to modeling real-world systems. The book is intended for undergraduate and graduate-level teaching in industrial engineering and other engineering specialties. It is also of use to industry practitioners, due to the inclusion of real-world applications, opening the door to advanced courses on both modeling and algorithm development within the industrial engineering and operations research fields.

Introduction to Linear Programming

Author: Leonid Nison Vaserstein
Publisher: Prentice Hall
ISBN: 0130359173
Release Date: 2003
Genre: Mathematics

For a one-semester course in Linear Programming for upper-level students with varying mathematical backgrounds. Written to include three different mathematical levels, this text strikes the necessary balance for a class consisting of students with varying mathematical backgrounds. It covers the basics of Linear Programs and also includes an appendix that develops many advanced topics in mathematical programming for students who plan to go on to graduate-level study in this field. Many exercises of varying difficulty provide introductory students the opportunity to progress through the material at a steady pace, while advanced students can proceed to the more challenging material.

Linear Programming

Author: Robert J Vanderbei
Publisher: Springer Science & Business Media
ISBN: 9781475756623
Release Date: 2013-06-29
Genre: Business & Economics

This book provides an introduction to optimization. It details constrained optimization, beginning with a substantial treatment of linear programming and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Coverage underscores the purpose of optimization: to solve practical problems on a computer. C programs that implement the major algorithms and JAVA tools are available online.