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Author : Uwe Zimmermann
Publisher :
ISBN 13 :
Total Pages : 13 pages
Book Rating : 4.:/5 (256 download)
Download or read book A primal dual method for algebraic linear programming written by Uwe Zimmermann and published by . This book was released on 1979 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Stephen J. Wright
Publisher : SIAM
ISBN 13 : 9781611971453
Total Pages : 309 pages
Book Rating : 4.9/5 (714 download)
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.
Author : Nimrod Megiddo
Publisher : Springer Science & Business Media
ISBN 13 : 1461396174
Total Pages : 164 pages
Book Rating : 4.4/5 (613 download)
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."
Author : Stanford University. Department of Operations Research. Systems Optimization Laboratory
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.F/5 ( download)
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:
Author : Manfred Padberg
Publisher : Springer Science & Business Media
ISBN 13 : 3662122731
Total Pages : 521 pages
Book Rating : 4.6/5 (621 download)
Download or read book Linear Optimization and Extensions written by Manfred Padberg and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Do you know M.Padberg's Linear Optimization and Extensions? [...] Now here is the continuation of it, discussing the solutions of all its exercises and with detailed analysis of the applications mentioned. Tell your students about it. [...] For those who strive for good exercises and case studies for LP this is an excellent volume." Acta Scientiarum Mathematicarum
Author : David P. Williamson
Publisher : Cambridge University Press
ISBN 13 : 9780521195270
Total Pages : 518 pages
Book Rating : 4.1/5 (952 download)
Download or read book The Design of Approximation Algorithms written by David P. Williamson and published by Cambridge University Press. This book was released on 2011-04-26 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.
Author : Gordon B. Hatfield
Publisher :
ISBN 13 :
Total Pages : 19 pages
Book Rating : 4.:/5 (227 download)
Download or read book Instructions for Use of the Primal-Dual Algorithm for the Solution of Non-Linear Programming Problems with Linear Constraints written by Gordon B. Hatfield and published by . This book was released on 1974 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: Instructions for solving the nonlinear problem with linear constraints using the primal-dual method are given. A brief exposition of the problem is followed by instructions concerning program input and output, deck set-up, and some comments on problem strategy.
Author : Yinyu Ye
Publisher : John Wiley & Sons
ISBN 13 : 1118030958
Total Pages : 440 pages
Book Rating : 4.1/5 (18 download)
Download or read book Interior Point Algorithms written by Yinyu Ye and published by John Wiley & Sons. This book was released on 2011-10-11 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Harold William Kuhn
Publisher : Princeton University Press
ISBN 13 : 1400881986
Total Pages : 346 pages
Book Rating : 4.4/5 (8 download)
Download or read book Linear Inequalities and Related Systems. (AM-38), Volume 38 written by Harold William Kuhn and published by Princeton University Press. This book was released on 2016-03-02 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Linear Inequalities and Related Systems. (AM-38), Volume 38, will be forthcoming.
Author : Florian Jarre
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.F/5 ( download)
Download or read book An Adaptive Primal-dual Method for Linear Programming written by Florian Jarre and published by . This book was released on 1991 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M.J. Panik
Publisher : Springer Science & Business Media
ISBN 13 : 1461334349
Total Pages : 502 pages
Book Rating : 4.4/5 (613 download)
Download or read book Linear Programming: Mathematics, Theory and Algorithms written by M.J. Panik and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.
Author : Gordon B. Hatfield
Publisher :
ISBN 13 :
Total Pages : 57 pages
Book Rating : 4.:/5 (227 download)
Download or read book Development and Evaluation of a Primal-Dual Method for the Solution of Non-Linear Programming Problems with Linear Constraints written by Gordon B. Hatfield and published by . This book was released on 1974 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general algorithm for solving the class of nonlinear programming problems that have linear constraints has been developed. The constraints can be either equations or inequalities and the variables can be free or non-negative. The objective function is assumed to be continuously differentiable. The algorithm is an 'effective' second-order method in that slow convergence is eliminated without requiring second partial derivations. It combines the desirable features of projection methods, conjugate gradient methods, and methods that solve LP problems to obtain feasible directions. Computational results on a wide variety of test problems are given. The comparison of two nonlinear programming algorithms--the primal-dual and the ricochet gradient--was employed as the vehicle for evaluating practices and standards employed in testing algorithms.
Author : Earl Jennings Bell
Publisher :
ISBN 13 :
Total Pages : 162 pages
Book Rating : 4.:/5 (21 download)
Download or read book Primal-dual Decomposition Programming written by Earl Jennings Bell and published by . This book was released on 1965 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: A primal-dual method for solving linear programs with a block-angular matrix structure is presented which employs the Decomposition Principle of Dantzig and Wolfe, who first studied this structure. Preliminary results indicate that the proposed method is more efficient than the standard decomposition method which uses the twophase simplex method to solve an equivalent 'extremal program' with a reduced basis size whose coefficients are generated through the solution of linear subprograms. By contrast, the proposed method employs a primal-dual method and the coefficients are generated through subprograms with nonlinear objectives. These subprograms involve the maximization of a quotient of two linear functions subject to linear constraints in nonegative variables. Such problems are known as linear-fractional, rational objective, or hyperbolic programs and can be solved as a variant of standard linear programming. Under the conditions imposed by the primal-dual method, special parametric techniques can be employed to take advantage of particular matrix structures, such as the transportation structure, exhibited by the subprograms. (Author).
Author : Thomas Francis Wagner
Publisher :
ISBN 13 :
Total Pages : 96 pages
Book Rating : 4.:/5 (322 download)
Download or read book The Primal-dual Algorithm for Linear Programming written by Thomas Francis Wagner and published by . This book was released on 1957 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : George Bernard Dantzig
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (713 download)
Download or read book Notes on Linear Programming written by George Bernard Dantzig and published by . This book was released on 1956 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jiming Peng
Publisher : Princeton University Press
ISBN 13 : 140082513X
Total Pages : 201 pages
Book Rating : 4.4/5 (8 download)
Download or read book Self-Regularity written by Jiming Peng and published by Princeton University Press. This book was released on 2009-01-10 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until now, there has been a notorious gap between the theory and practical performance of these two strategies. This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the notion of the self-regularity of a function. The authors deal with linear optimization, nonlinear complementarity problems, semidefinite optimization, and second-order conic optimization problems. The framework also covers large classes of linear complementarity problems and convex optimization. The algorithm considered can be interpreted as a path-following method or a potential reduction method. Starting from a primal-dual strictly feasible point, the algorithm chooses a search direction defined by some Newton-type system derived from the self-regular proximity. The iterate is then updated, with the iterates staying in a certain neighborhood of the central path until an approximate solution to the problem is found. By extensively exploring some intriguing properties of self-regular functions, the authors establish that the complexity of large-update IPMs can come arbitrarily close to the best known iteration bounds of IPMs. Researchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work.
Author : Michael C. Ferris
Publisher : SIAM
ISBN 13 : 0898716438
Total Pages : 270 pages
Book Rating : 4.8/5 (987 download)
Download or read book Linear Programming with MATLAB written by Michael C. Ferris and published by SIAM. This book was released on 2007-01-01 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to linear programming using MATLAB® software to elucidate the development of algorithms and theory. Exercises are included in each chapter, and additional information is provided in two appendices and an accompanying Web site. Only a basic knowledge of linear algebra and calculus is required.
