New Algorithmic Approaches For Semidefinite Programming With Applications To Combinatorial Optimization
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New Algorithmic Approaches For Semidefinite Programming With Applications To Combinatorial Optimization
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Author : Samuel A. Burer
language : en
Publisher:
Release Date : 2001
New Algorithmic Approaches For Semidefinite Programming With Applications To Combinatorial Optimization written by Samuel A. Burer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Algorithms categories.
New Algorithmic Approaches For Semidefinite Programming With Applications To Combinatorial Optimization
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Author : Samuel A. Burer
language : en
Publisher:
Release Date : 2001
New Algorithmic Approaches For Semidefinite Programming With Applications To Combinatorial Optimization written by Samuel A. Burer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Linear programming categories.
Aspects Of Semidefinite Programming
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Author : E. de Klerk
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Aspects Of Semidefinite Programming written by E. de Klerk 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 2006-04-18 with Computers categories.
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.
Polyhedral And Semidefinite Programming Methods In Combinatorial Optimization
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Author : Levent Tunçel
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-05-05
Polyhedral And Semidefinite Programming Methods In Combinatorial Optimization written by Levent Tunçel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-05 with Mathematics categories.
Since the early 1960s, polyhedral methods have played a central role in both the theory and practice of combinatorial optimization. Since the early 1990s, a new technique, semidefinite programming, has been increasingly applied to some combinatorial optimization problems. The semidefinite programming problem is the problem of optimizing a linear function of matrix variables, subject to finitely many linear inequalities and the positive semidefiniteness condition on some of the matrix variables. On certain problems, such as maximum cut, maximum satisfiability, maximum stable set and geometric representations of graphs, semidefinite programming techniques yield important new results. This monograph provides the necessary background to work with semidefinite optimization techniques, usually by drawing parallels to the development of polyhedral techniques and with a special focus on combinatorial optimization, graph theory and lift-and-project methods. It allows the reader to rigorously develop the necessary knowledge, tools and skills to work in the area that is at the intersection of combinatorial optimization and semidefinite optimization. A solid background in mathematics at the undergraduate level and some exposure to linear optimization are required. Some familiarity with computational complexity theory and the analysis of algorithms would be helpful. Readers with these prerequisites will appreciate the important open problems and exciting new directions as well as new connections to other areas in mathematical sciences that the book provides.
Topics In Semidefinite And Interior Point Methods
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Author : Panos M. Pardalos
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Topics In Semidefinite And Interior Point Methods written by Panos M. Pardalos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Interior-point methods categories.
This volume presents refereed papers presented at the workshop Semidefinite Programming and Interior-Point Approaches for Combinatorial Problems: held at The Fields Institute in May 1996. Semidefinite programming (SDP) is a generalization of linear programming (LP) in that the non-negativity constraints on the variables is replaced by a positive semidefinite constraint on matrix variables. Many of the elegant theoretical properties and powerful solution techniques follow through from LP to SDP. In particular, the primal-dual interior-point methods, which are currently so successful for LP, can be used to efficiently solve SDP problems. In addition to the theoretical and algorithmic questions, SDP has found many important applications in combinatorial optimization, control theory and other areas of mathematical programming. The papers in this volume cover a wide spectrum of recent developments in SDP. The volume would be suitable as a textbook for advanced courses in optimization. It is intended for graduate students and researchers in mathematics, computer science, engineering and operations.
Approximation Algorithms And Semidefinite Programming
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Author : Bernd Gärtner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-10
Approximation Algorithms And Semidefinite Programming written by Bernd Gärtner 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 2012-01-10 with Mathematics categories.
Semidefinite programs constitute one of the largest classes of optimization problems that can be solved with reasonable efficiency - both in theory and practice. They play a key role in a variety of research areas, such as combinatorial optimization, approximation algorithms, computational complexity, graph theory, geometry, real algebraic geometry and quantum computing. This book is an introduction to selected aspects of semidefinite programming and its use in approximation algorithms. It covers the basics but also a significant amount of recent and more advanced material. There are many computational problems, such as MAXCUT, for which one cannot reasonably expect to obtain an exact solution efficiently, and in such case, one has to settle for approximate solutions. For MAXCUT and its relatives, exciting recent results suggest that semidefinite programming is probably the ultimate tool. Indeed, assuming the Unique Games Conjecture, a plausible but as yet unproven hypothesis, it was shown that for these problems, known algorithms based on semidefinite programming deliver the best possible approximation ratios among all polynomial-time algorithms. This book follows the “semidefinite side” of these developments, presenting some of the main ideas behind approximation algorithms based on semidefinite programming. It develops the basic theory of semidefinite programming, presents one of the known efficient algorithms in detail, and describes the principles of some others. It also includes applications, focusing on approximation algorithms.
Nonlinear Assignment Problems
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Author : Panos M. Pardalos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Nonlinear Assignment Problems written by Panos M. Pardalos 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 2013-03-09 with Computers categories.
Nonlinear Assignment Problems (NAPs) are natural extensions of the classic Linear Assignment Problem, and despite the efforts of many researchers over the past three decades, they still remain some of the hardest combinatorial optimization problems to solve exactly. The purpose of this book is to provide in a single volume, major algorithmic aspects and applications of NAPs as contributed by leading international experts. The chapters included in this book are concerned with major applications and the latest algorithmic solution approaches for NAPs. Approximation algorithms, polyhedral methods, semidefinite programming approaches and heuristic procedures for NAPs are included, while applications of this problem class in the areas of multiple-target tracking in the context of military surveillance systems, of experimental high energy physics, and of parallel processing are presented. Audience: Researchers and graduate students in the areas of combinatorial optimization, mathematical programming, operations research, physics, and computer science.
Handbook Of Semidefinite Programming
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Author : Henry Wolkowicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Handbook Of Semidefinite Programming written by Henry Wolkowicz 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 2012-12-06 with Business & Economics categories.
Semidefinite programming (SDP) is one of the most exciting and active research areas in optimization. It has and continues to attract researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, control theory, and statistics. This tremendous research activity has been prompted by the discovery of important applications in combinatorial optimization and control theory, the development of efficient interior-point algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory. The Handbook of Semidefinite Programming offers an advanced and broad overview of the current state of the field. It contains nineteen chapters written by the leading experts on the subject. The chapters are organized in three parts: Theory, Algorithms, and Applications and Extensions.
Interior Point Methods In Semidefinite Programming With Applications To Combinatorial Optimization
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Author : International Computer Science Institute
language : en
Publisher:
Release Date : 1993
Interior Point Methods In Semidefinite Programming With Applications To Combinatorial Optimization written by International Computer Science Institute and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Combinatorial optimization categories.
Abstract: "We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity also carrying over in a similar fashion. Finally we study the significance of these results in a variety of combinatorial optimization problems including the general 0-1 integer programs, the maximum clique and maximum stable set problems in perfect graphs, the maximum k-partite subgraph problem in graphs, and various graph partitioning and cut problems. As a result, we present barrier oracles for certain combinatorial optimization problems (in particular, clique and stable set problem for perfect graphs) whose linear programming formulation requires exponentially many inequalities. Existence of such barrier oracles refutes the commonly believed notion that in order to solve a combinatorial optimization problem with interior point methods, one needs its linear programming formulation explicitly."
Handbook Of Combinatorial Optimization
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Author : Ding-Zhu Du
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Handbook Of Combinatorial Optimization written by Ding-Zhu Du 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.
Combinatorial (or discrete) optimization is one of the most active fields in the interface of operations research, computer science, and applied math ematics. Combinatorial optimization problems arise in various applications, including communications network design, VLSI design, machine vision, air line crew scheduling, corporate planning, computer-aided design and man ufacturing, database query design, cellular telephone frequency assignment, constraint directed reasoning, and computational biology. Furthermore, combinatorial optimization problems occur in many diverse areas such as linear and integer programming, graph theory, artificial intelligence, and number theory. All these problems, when formulated mathematically as the minimization or maximization of a certain function defined on some domain, have a commonality of discreteness. Historically, combinatorial optimization starts with linear programming. Linear programming has an entire range of important applications including production planning and distribution, personnel assignment, finance, alloca tion of economic resources, circuit simulation, and control systems. Leonid Kantorovich and Tjalling Koopmans received the Nobel Prize (1975) for their work on the optimal allocation of resources. Two important discover ies, the ellipsoid method (1979) and interior point approaches (1984) both provide polynomial time algorithms for linear programming. These algo rithms have had a profound effect in combinatorial optimization. Many polynomial-time solvable combinatorial optimization problems are special cases of linear programming (e.g. matching and maximum flow). In addi tion, linear programming relaxations are often the basis for many approxi mation algorithms for solving NP-hard problems (e.g. dual heuristics).