Primal Barrier Methods For Linear Programming

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Primal Barrier Methods for Linear Programming

Author : Aeneas Marxen
Publisher :
ISBN 13 :
Total Pages : 86 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Primal Barrier Methods for Linear Programming by : Aeneas Marxen

Download or read book Primal Barrier Methods for Linear Programming written by Aeneas Marxen and published by . This book was released on 1989 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "The linear program min c[superscript T]x subject to Ax=b, x [greater than or equal to] 0, is solved by the projected Newton barrier method. The method consists of solving a sequence of subproblems of the form [formula] subject to Ax=b. Extensions for upper bounds, free and fixed variables are given. A linear modification is made to the logarithmic barrier function, which results in the solution being bounded in all cases. It also facilitates the provision of a good starting point. The solution of each subproblem involves repeatedly computing a search direction and taking a step along this direction. Ways to find an initial feasible solution, step sizes and convergence criteria are discussed.

Primal-dual Methods for Linear Programming

Author : Stanford University. Department of Operations Research. Systems Optimization Laboratory
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Primal-dual Methods for Linear Programming by : Stanford University. Department of Operations Research. Systems Optimization Laboratory

Download or read book Primal-dual Methods for Linear Programming written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and published by . This book was released on 1991 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Progress in Mathematical Programming

Author : Nimrod Megiddo
Publisher : Springer Science & Business Media
ISBN 13 : 1461396174
Total Pages : 164 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Progress in Mathematical Programming by : Nimrod Megiddo

Download or read book Progress in Mathematical Programming written by Nimrod Megiddo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Primal-dual Algorithms for Linear Programming Based on the Logarithmic Barrier Method

Author : B. Jansen
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (461 download)

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Book Synopsis Primal-dual Algorithms for Linear Programming Based on the Logarithmic Barrier Method by : B. Jansen

Download or read book Primal-dual Algorithms for Linear Programming Based on the Logarithmic Barrier Method written by B. Jansen and published by . This book was released on 1992 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Solving Regularized Linear Programs Using Barrier Methods and KKT Systems

Author : Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization Laboratory
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Solving Regularized Linear Programs Using Barrier Methods and KKT Systems by : Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization Laboratory

Download or read book Solving Regularized Linear Programs Using Barrier Methods and KKT Systems written by Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization Laboratory and published by . This book was released on 1996 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We discuss methods for solving the key linear equations (KKT systems) within primal-dual barrier methods for linear programming. To allow sparse indefinite Cholesky-type factorizations of the KKT systems, we perturb the problem slightly. Perturbations improve the stability of the Cholesky factorizations, but affect the efficiency of the cross-over to simplex (to obtain a basic solution to the original problem). We explore these effects by running OSL on the larger Netlib examples."

Solving Reduced KKT Systems in Barrier Methods for Linear and Quadratic Programming

Author : Stanford University. Department of Operations Research. Systems Optimization Laboratory
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Solving Reduced KKT Systems in Barrier Methods for Linear and Quadratic Programming by : Stanford University. Department of Operations Research. Systems Optimization Laboratory

Download or read book Solving Reduced KKT Systems in Barrier Methods for Linear and Quadratic Programming written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and published by . This book was released on 1991 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Linear Programming 2

Author : George B. Dantzig
Publisher : Springer Science & Business Media
ISBN 13 : 0387215697
Total Pages : 461 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Linear Programming 2 by : George B. Dantzig

Download or read book Linear Programming 2 written by George B. Dantzig and published by Springer Science & Business Media. This book was released on 2006-04-28 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: George Dantzig is widely regarded as the founder of this subject with his invention of the simplex algorithm in the 1940's. In this second volume, the theory of the items discussed in the first volume is expanded to include such additional advanced topics as variants of the simplex method; interior point methods, GUB, decomposition, integer programming, and game theory. Graduate students in the fields of operations research, industrial engineering and applied mathematics will thus find this volume of particular interest.

Primal-dual Interior-Point Methods

Author : Stephen J. Wright
Publisher : SIAM
ISBN 13 : 9781611971453
Total Pages : 309 pages
Book Rating : 4.9/5 (714 download)

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Book Synopsis Primal-dual Interior-Point Methods by : Stephen J. Wright

Download or read book Primal-dual Interior-Point Methods written by Stephen J. Wright and published by SIAM. This book was released on 1997-01-01 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Linear and Nonlinear Programming

Author : David G. Luenberger
Publisher : Springer Nature
ISBN 13 : 3030854507
Total Pages : 609 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Linear and Nonlinear Programming by : David G. Luenberger

Download or read book Linear and Nonlinear Programming written by David G. Luenberger and published by Springer Nature. This book was released on 2021-10-31 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

High Performance Algorithms and Software in Nonlinear Optimization

Author : Renato de Leone
Publisher : Springer Science & Business Media
ISBN 13 : 1461332796
Total Pages : 379 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis High Performance Algorithms and Software in Nonlinear Optimization by : Renato de Leone

Download or read book High Performance Algorithms and Software in Nonlinear Optimization written by Renato de Leone and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a selection of papers presented at the conference on High Performance Software for Nonlinear Optimization (HPSN097) which was held in Ischia, Italy, in June 1997. The rapid progress of computer technologies, including new parallel architec tures, has stimulated a large amount of research devoted to building software environments and defining algorithms able to fully exploit this new computa tional power. In some sense, numerical analysis has to conform itself to the new tools. The impact of parallel computing in nonlinear optimization, which had a slow start at the beginning, seems now to increase at a fast rate, and it is reasonable to expect an even greater acceleration in the future. As with the first HPSNO conference, the goal of the HPSN097 conference was to supply a broad overview of the more recent developments and trends in nonlinear optimization, emphasizing the algorithmic and high performance software aspects. Bringing together new computational methodologies with theoretical ad vances and new computer technologies is an exciting challenge that involves all scientists willing to develop high performance numerical software. This book contains several important contributions from different and com plementary standpoints. Obviously, the articles in the book do not cover all the areas of the conference topic or all the most recent developments, because of the large number of new theoretical and computational ideas of the last few years.

Interior Point Methods for Linear Optimization

Author : Cornelis Roos
Publisher : Springer Science & Business Media
ISBN 13 : 0387263799
Total Pages : 501 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Interior Point Methods for Linear Optimization by : Cornelis Roos

Download or read book Interior Point Methods for Linear Optimization written by Cornelis Roos and published by Springer Science & Business Media. This book was released on 2006-02-08 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stable Reduction to KKT Systems in Barrier Methods for Linear and Quadratic Programming

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Book Synopsis Stable Reduction to KKT Systems in Barrier Methods for Linear and Quadratic Programming by : Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization Laboratory

Download or read book Stable Reduction to KKT Systems in Barrier Methods for Linear and Quadratic Programming written by Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization Laboratory and published by . This book was released on 1996 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We discuss methods for solving the key linear equations within primal-dual barrier methods for linear and quadratic programming. Following Freund and Jarre, we explore methods for reducing the Newton equations to 2 X 2 block systems (KKT systems) in a stable manner. Some methods require partitioning the variables into two or more parts, but a simpler approach is derived and recommended. To justify symmetrizing the KKT systems, we assume the use of a sparse solver whose numerical properties are independent of row and column scaling. In particular, we regularize the problem and use indefinite Cholesky-type factorizations. An implementation within OSL is tested on the larger NETLIB examples."

Linear and Nonlinear Optimization

Author : Richard W. Cottle
Publisher : Springer
ISBN 13 : 1493970550
Total Pages : 644 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Linear and Nonlinear Optimization by : Richard W. Cottle

Download or read book Linear and Nonlinear Optimization written by Richard W. Cottle and published by Springer. This book was released on 2017-06-11 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Linear and Nonlinear Optimization

Author : Igor Griva
Publisher : SIAM
ISBN 13 : 0898717736
Total Pages : 743 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Linear and Nonlinear Optimization by : Igor Griva

Download or read book Linear and Nonlinear Optimization written by Igor Griva and published by SIAM. This book was released on 2009-01-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to the applications, theory, and algorithms of linear and nonlinear optimization. The emphasis is on practical aspects - discussing modern algorithms, as well as the influence of theory on the interpretation of solutions or on the design of software. The book includes several examples of realistic optimization models that address important applications. The succinct style of this second edition is punctuated with numerous real-life examples and exercises, and the authors include accessible explanations of topics that are not often mentioned in textbooks, such as duality in nonlinear optimization, primal-dual methods for nonlinear optimization, filter methods, and applications such as support-vector machines. The book is designed to be flexible. It has a modular structure, and uses consistent notation and terminology throughout. It can be used in many different ways, in many different courses, and at many different levels of sophistication.

Aspects of Semidefinite Programming

Author : E. de Klerk
Publisher : Springer Science & Business Media
ISBN 13 : 0306478196
Total Pages : 287 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Aspects of Semidefinite Programming by : E. de Klerk

Download or read book Aspects of Semidefinite Programming written by E. de Klerk and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semidefinite programming has been described as linear programming for the year 2000. It is an exciting new branch of mathematical programming, due to important applications in control theory, combinatorial optimization and other fields. Moreover, the successful interior point algorithms for linear programming can be extended to semidefinite programming. In this monograph the basic theory of interior point algorithms is explained. This includes the latest results on the properties of the central path as well as the analysis of the most important classes of algorithms. Several "classic" applications of semidefinite programming are also described in detail. These include the Lovász theta function and the MAX-CUT approximation algorithm by Goemans and Williamson. Audience: Researchers or graduate students in optimization or related fields, who wish to learn more about the theory and applications of semidefinite programming.

Scientific and Technical Aerospace Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.:/5 (3 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1991 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Developments Arising from Linear Programming

Author : Jeffrey C. Lagarias
Publisher : American Mathematical Soc.
ISBN 13 : 0821851217
Total Pages : 360 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mathematical Developments Arising from Linear Programming by : Jeffrey C. Lagarias

Download or read book Mathematical Developments Arising from Linear Programming written by Jeffrey C. Lagarias and published by American Mathematical Soc.. This book was released on 1990 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been much recent work in linear and non-linear programming centred on understanding and extending the ideas underlying Karmarkar's interior-point linear programming algorithm. This volume is the result of an AMS conference on mathematical developments arising from linear programming.