A Unified Approach To Interior Point Algorithms For Linear Complementarity Problems
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A Unified Approach To Interior Point Algorithms For Linear Complementarity Problems
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Author : Masakazu Kojima
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-09-25
A Unified Approach To Interior Point Algorithms For Linear Complementarity Problems written by Masakazu Kojima 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 1991-09-25 with Language Arts & Disciplines categories.
Following Karmarkar's 1984 linear programming algorithm, numerous interior-point algorithms have been proposed for various mathematical programming problems such as linear programming, convex quadratic programming and convex programming in general. This monograph presents a study of interior-point algorithms for the linear complementarity problem (LCP) which is known as a mathematical model for primal-dual pairs of linear programs and convex quadratic programs. A large family of potential reduction algorithms is presented in a unified way for the class of LCPs where the underlying matrix has nonnegative principal minors (P0-matrix). This class includes various important subclasses such as positive semi-definite matrices, P-matrices, P*-matrices introduced in this monograph, and column sufficient matrices. The family contains not only the usual potential reduction algorithms but also path following algorithms and a damped Newton method for the LCP. The main topics are global convergence, global linear convergence, and the polynomial-time convergence of potential reduction algorithms included in the family.
A Unified Approach To Interior Point Algorithms For Linear Complementarity Problems
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Author : Masakazu Kojima
language : en
Publisher:
Release Date : 2014-01-15
A Unified Approach To Interior Point Algorithms For Linear Complementarity Problems written by Masakazu Kojima and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
The Linear Complementarity Problem
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Author : Richard W. Cottle
language : en
Publisher: SIAM
Release Date : 2009-08-27
The Linear Complementarity Problem written by Richard W. Cottle and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-27 with Mathematics categories.
A revised edition of the standard reference on the linear complementarity problem.
Acta Numerica 1993 Volume 2
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Author : Arieh Iserles
language : en
Publisher: Cambridge University Press
Release Date : 1993-04-30
Acta Numerica 1993 Volume 2 written by Arieh Iserles and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-04-30 with Mathematics categories.
Continuing the tradition established with the 1992 volume, this 1993's Acta Numerica presents six invited papers on a broad range of topics from numerical analysis. Papers treat each topic at a level intelligible by any numerical analyst from graduate student to professional.
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.
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.
Interior Point Polynomial Algorithms In Convex Programming
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Author : Yurii Nesterov
language : en
Publisher: SIAM
Release Date : 1994-01-01
Interior Point Polynomial Algorithms In Convex Programming written by Yurii Nesterov and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.
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.
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.
The Linear Complementarity Problem
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Author : Richard W. Cottle
language : en
Publisher: SIAM
Release Date : 1992-01-01
The Linear Complementarity Problem written by Richard W. Cottle and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
Awarded the Frederick W. Lanchester Prize in 1994 for its valuable contributions to operations research and the management sciences, this mathematically rigorous book remains the standard reference on the linear complementarity problem. Readers will find a comprehensive treatment of the computation of equilibria arising from engineering, economics, and finance; chapter-ending exercises and "Notes and References" sections that make it equally useful for a graduate-level course or for self-study; corrections and revisions of difficult passages from the 1992 edition; and an updated bibliography. Audience: researchers and graduate students in fields including optimization, game theory, and finance, and diverse engineering disciplines, especially computer science and mechanical engineering.
Interior Point Methods Of Mathematical Programming
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Author : Tamás Terlaky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Interior Point Methods Of Mathematical Programming written by Tamás 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 2013-12-01 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).