Interior Point Methods For Linear Optimization

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Interior Point Methods For Linear Optimization

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Author : Cornelis Roos
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-08

Interior Point Methods For Linear Optimization written by Cornelis Roos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-08 with Mathematics categories.

Interior Point Methods for Linear Optimization is a comprehensive, thorough textbook on interior point methods (IPMs). The era of 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 gives a comprehensive review of the main results of more than a decade of IPM research. Numerous exercises are provided to aid in understanding the material.

Primal Dual Interior Point Methods

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Author : Stephen J. Wright
language : en
Publisher: SIAM
Release Date : 1997-01-01

Primal Dual Interior Point Methods written by Stephen J. Wright and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Technology & Engineering categories.

In the past decade, primal-dual algorithms have emerged as the most important and useful algorithms from the interior-point class. This book presents the major primal-dual algorithms for linear programming in straightforward terms. A thorough description of the theoretical properties of these methods is given, as are a discussion of practical and computational aspects and a summary of current software. This is an excellent, timely, and well-written work. The major primal-dual algorithms covered in this book are path-following algorithms (short- and long-step, predictor-corrector), potential-reduction algorithms, and infeasible-interior-point algorithms. A unified treatment of superlinear convergence, finite termination, and detection of infeasible problems is presented. Issues relevant to practical implementation are also discussed, including sparse linear algebra and a complete specification of Mehrotra's predictor-corrector algorithm. Also treated are extensions of primal-dual algorithms to more general problems such as monotone complementarity, semidefinite programming, and general convex programming problems.

Interior Point Methods Of Mathematical Programming

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Author : Tamas Terlaky
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-09-30

Interior Point Methods Of Mathematical Programming written by Tamas Terlaky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-09-30 with Mathematics categories.

One has to make everything as simple as possible but, never more simple. Albert Einstein Discovery consists of seeing what every body has seen and thinking what nobody has thought. Albert S. ent_Gyorgy; The primary goal of this book is to provide an introduction to the theory of Interior Point Methods (IPMs) in Mathematical Programming. At the same time, we try to present a quick overview of the impact of extensions of IPMs on smooth nonlinear optimization and to demonstrate the potential of IPMs for solving difficult practical problems. The Simplex Method has dominated the theory and practice of mathematical pro gramming since 1947 when Dantzig discovered it. In the fifties and sixties several attempts were made to develop alternative solution methods. At that time the prin cipal base of interior point methods was also developed, for example in the work of Frisch (1955), Caroll (1961), Huard (1967), Fiacco and McCormick (1968) and Dikin (1967). In 1972 Klee and Minty made explicit that in the worst case some variants of the simplex method may require an exponential amount of work to solve Linear Programming (LP) problems. This was at the time when complexity theory became a topic of great interest. People started to classify mathematical programming prob lems as efficiently (in polynomial time) solvable and as difficult (NP-hard) problems. For a while it remained open whether LP was solvable in polynomial time or not. The break-through resolution ofthis problem was obtained by Khachijan (1989).

Infeasible Interior Point Methods For Linear And Convex Programming

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Author : Reha Hüsnü Tütüncü
language : en
Publisher:
Release Date : 1996

Infeasible Interior Point Methods For Linear And Convex Programming written by Reha Hüsnü Tütüncü and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.

Theory And Algorithms For Linear Optimization

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Author : Cornelis Roos
language : en
Publisher:
Release Date : 1997-03-04

Theory And Algorithms For Linear Optimization written by Cornelis Roos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-03-04 with Mathematics categories.

The approach to LO in this book is new in many aspects. In particular the IPM based development of duality theory is surprisingly elegant. The algorithmic parts of the book contain a complete discussion of many algorithmic variants, including predictor-corrector methods, partial updating, higher order methods and sensitivity and parametric analysis.

Interior Point Techniques In Optimization

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Author : B. Jansen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Interior Point Techniques In Optimization written by B. Jansen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

Operations research and mathematical programming would not be as advanced today without the many advances in interior point methods during the last decade. These methods can now solve very efficiently and robustly large scale linear, nonlinear and combinatorial optimization problems that arise in various practical applications. The main ideas underlying interior point methods have influenced virtually all areas of mathematical programming including: analyzing and solving linear and nonlinear programming problems, sensitivity analysis, complexity analysis, the analysis of Newton's method, decomposition methods, polynomial approximation for combinatorial problems etc. This book covers the implications of interior techniques for the entire field of mathematical programming, bringing together many results in a uniform and coherent way. For the topics mentioned above the book provides theoretical as well as computational results, explains the intuition behind the main ideas, gives examples as well as proofs, and contains an extensive up-to-date bibliography. Audience: The book is intended for students, researchers and practitioners with a background in operations research, mathematics, mathematical programming, or statistics.

A Mathematical View Of Interior Point Methods In Convex Optimization

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Author : James Renegar
language : en
Publisher: SIAM
Release Date : 2001-01-01

A Mathematical View Of Interior Point Methods In Convex Optimization written by James Renegar and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.

Takes the reader who knows little of interior-point methods to within sight of the research frontier.

Exploring Interior Point Linear Programming

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Author : Ami Arbel
language : en
Publisher: MIT Press
Release Date : 1993

Exploring Interior Point Linear Programming written by Ami Arbel and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Computers categories.

This book provides practitioners as well as students of this general methodology with an easily accessible introduction to the new class of algorithms known as interior-point methods for linear programming.

Encyclopedia Of Optimization

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Author : Christodoulos A. Floudas
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-04

Encyclopedia Of Optimization written by Christodoulos A. Floudas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-04 with Mathematics categories.

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Interior Point Algorithms

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Author : Yinyu Ye
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-11

Interior Point Algorithms written by Yinyu Ye and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-11 with Mathematics categories.

The first comprehensive review of the theory and practice of one oftoday's most powerful optimization techniques. The explosive growth of research into and development of interiorpoint algorithms over the past two decades has significantlyimproved the complexity of linear programming and yielded some oftoday's most sophisticated computing techniques. This book offers acomprehensive and thorough treatment of the theory, analysis, andimplementation of this powerful computational tool. Interior Point Algorithms provides detailed coverage of all basicand advanced aspects of the subject. Beginning with an overview offundamental mathematical procedures, Professor Yinyu Ye movesswiftly on to in-depth explorations of numerous computationalproblems and the algorithms that have been developed to solve them.An indispensable text/reference for students and researchers inapplied mathematics, computer science, operations research,management science, and engineering, Interior Point Algorithms: * Derives various complexity results for linear and convexprogramming * Emphasizes interior point geometry and potential theory * Covers state-of-the-art results for extension, implementation,and other cutting-edge computational techniques * Explores the hottest new research topics, including nonlinearprogramming and nonconvex optimization.