A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems
A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems

Author: Masakazu Kojima

Publisher: Springer Science & Business Media

Published: 1991-09-25

Total Pages: 124

ISBN-13: 9783540545095

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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.

Primal-dual Interior-Point Methods
Primal-dual Interior-Point Methods

Author: Stephen J. Wright

Publisher: SIAM

Published: 1997-01-01

Total Pages: 309

ISBN-13: 9781611971453

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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 Algorithms
Interior Point Algorithms

Author: Yinyu Ye

Publisher: John Wiley & Sons

Published: 2011-10-11

Total Pages: 440

ISBN-13: 1118030958

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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.

High Performance Optimization
High Performance Optimization

Author: Hans Frenk

Publisher: Springer Science & Business Media

Published: 2000

Total Pages: 506

ISBN-13: 9780792360131

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For a long time the techniques of solving linear optimization (LP) problems improved only marginally. Fifteen years ago, however, a revolutionary discovery changed everything. A new `golden age' for optimization started, which is continuing up to the current time. What is the cause of the excitement? Techniques of linear programming formed previously an isolated body of knowledge. Then suddenly a tunnel was built linking it with a rich and promising land, part of which was already cultivated, part of which was completely unexplored. These revolutionary new techniques are now applied to solve conic linear problems. This makes it possible to model and solve large classes of essentially nonlinear optimization problems as efficiently as LP problems. This volume gives an overview of the latest developments of such `High Performance Optimization Techniques'. The first part is a thorough treatment of interior point methods for semidefinite programming problems. The second part reviews today's most exciting research topics and results in the area of convex optimization. Audience: This volume is for graduate students and researchers who are interested in modern optimization techniques.

Interior Point Methods for Linear Optimization
Interior Point Methods for Linear Optimization

Author: Cornelis Roos

Publisher: Springer Science & Business Media

Published: 2006-02-08

Total Pages: 501

ISBN-13: 0387263799

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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.

Encyclopedia of Optimization
Encyclopedia of Optimization

Author: Christodoulos A. Floudas

Publisher: Springer Science & Business Media

Published: 2008-09-04

Total Pages: 4646

ISBN-13: 0387747583

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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".

Advances in Optimization and Numerical Analysis
Advances in Optimization and Numerical Analysis

Author: S. Gomez

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 285

ISBN-13: 9401583307

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In January 1992, the Sixth Workshop on Optimization and Numerical Analysis was held in the heart of the Mixteco-Zapoteca region, in the city of Oaxaca, Mexico, a beautiful and culturally rich site in ancient, colonial and modern Mexican civiliza tion. The Workshop was organized by the Numerical Analysis Department at the Institute of Research in Applied Mathematics of the National University of Mexico in collaboration with the Mathematical Sciences Department at Rice University, as were the previous ones in 1978, 1979, 1981, 1984 and 1989. As were the third, fourth, and fifth workshops, this one was supported by a grant from the Mexican National Council for Science and Technology, and the US National Science Foundation, as part of the joint Scientific and Technical Cooperation Program existing between these two countries. The participation of many of the leading figures in the field resulted in a good representation of the state of the art in Continuous Optimization, and in an over view of several topics including Numerical Methods for Diffusion-Advection PDE problems as well as some Numerical Linear Algebraic Methods to solve related pro blems. This book collects some of the papers given at this Workshop.

Progress in Mathematical Programming
Progress in Mathematical Programming

Author: Nimrod Megiddo

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 164

ISBN-13: 1461396174

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The starting point of this volume was a conference entitled "Progress in Mathematical Programming," held at the Asilomar Conference Center in Pacific Grove, California, March 1-4, 1987. The main topic of the conference was developments in the theory and practice of linear programming since Karmarkar's algorithm. There were thirty presentations and approximately fifty people attended. Presentations included new algorithms, new analyses of algorithms, reports on computational experience, and some other topics related to the practice of mathematical programming. Interestingly, most of the progress reported at the conference was on the theoretical side. Several new polynomial algorithms for linear program ming were presented (Barnes-Chopra-Jensen, Goldfarb-Mehrotra, Gonzaga, Kojima-Mizuno-Yoshise, Renegar, Todd, Vaidya, and Ye). Other algorithms presented were by Betke-Gritzmann, Blum, Gill-Murray-Saunders-Wright, Nazareth, Vial, and Zikan-Cottle. Efforts in the theoretical analysis of algo rithms were also reported (Anstreicher, Bayer-Lagarias, Imai, Lagarias, Megiddo-Shub, Lagarias, Smale, and Vanderbei). Computational experiences were reported by Lustig, Tomlin, Todd, Tone, Ye, and Zikan-Cottle. Of special interest, although not in the main direction discussed at the conference, was the report by Rinaldi on the practical solution of some large traveling salesman problems. At the time of the conference, it was still not clear whether the new algorithms developed since Karmarkar's algorithm would replace the simplex method in practice. Alan Hoffman presented results on conditions under which linear programming problems can be solved by greedy algorithms."

Fuzzy Information and Engineering
Fuzzy Information and Engineering

Author: Bingyuan Cao

Publisher: Springer Science & Business Media

Published: 2009-01-04

Total Pages: 678

ISBN-13: 3540889140

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This book is the proceedings of the Third Annual Conference on Fuzzy Information and Engineering (ACFIE2008) from Dec. 5-10, 2008 in Haikou, China. The conf- ence proceedingsis published by Springer-Verlag(Advancesin Soft Computing,ISSN: 1615-3871). This year, we have received 155 submissions. Each paper has undergone a rigorous review process. Only high-quality papers are included. The Third Annual Conference on Fuzzy Information and Engineering (ACFIE2008), built on the success of previous conferences,the ACFIE2005 (Guangzhou,China), is a major symposium for scientists, engineers and practitioners in China to present their updated results, ideas, devel- ments and applications in all areas of fuzzy information and engineering. It aims to strengthen relations between industry research laboratoriesand universities, and to c- ate a primary symposium for world scientists in fuzzy ?elds as follows: 1) Fuzzy intelligence, neural networks and optimal; 2) Fuzzy algebra; 3) Fuzzy analysis; 4) Fuzzy systems and logic; 5) Fuzzy topology and measure; 6)Fuzzy probability, control, forecasting and decision-making; 7) Fuzzy clustering and fuzzy algorithms; 8) Application in fuzzy sets; 9) Rough sets and its application; etc. This book contains 80 papers, divided into nine main parts: In Section I, we have 9 papers on “fuzzy intelligence, neural networks and optimal”. In Section II, we have 11 papers on “fuzzy algebra”. In Section III, we have 9 papers on “fuzzy analysis”. In Section IV, we have 9 papers on “fuzzy systems and logic”. In Section V, we have 9 papers on “fuzzy topology and measure”.