A Note on the Primal-dual Affine Scaling Algorithms PDF Download
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Author: Levent Tuncel
Publisher:
ISBN:
Category :
Languages : en
Pages : 32
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Book Description
Author: Levent Tuncel
Publisher:
ISBN:
Category :
Languages : en
Pages : 32
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Book Description
Author: Stephen J. Wright
Publisher: SIAM
ISBN: 089871382X
Category : Technology & Engineering
Languages : en
Pages : 293
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Book Description
Presents the major primal-dual algorithms for linear programming. A thorough, straightforward description of the theoretical properties of these methods.
Author: Xiaodong Yang
Publisher:
ISBN:
Category :
Languages : en
Pages : 122
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
Author: Jos Fredrik Sturm
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
Author: Jiming Peng
Publisher: Princeton University Press
ISBN: 140082513X
Category : Mathematics
Languages : en
Pages : 208
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Book Description
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: Nimrod Megiddo
Publisher: Springer Science & Business Media
ISBN: 1461396174
Category : Mathematics
Languages : en
Pages : 164
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Book Description
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: Lawrence Nazareth
Publisher: Springer Science & Business Media
ISBN: 9780387211558
Category : Mathematics
Languages : en
Pages : 136
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Book Description
This book introduces a general audience to the main facets of optimization. Very little mathematical background is assumed. It should appeal to students, teachers, and a general audience interested in how optimization affects their everyday life, such as people in business.
Author: Jos Fredrik Sturm
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
Author: E. de Klerk
Publisher: Springer Science & Business Media
ISBN: 0306478196
Category : Computers
Languages : en
Pages : 287
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Book Description
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.
