Aspects Of Semidefinite Programming

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Aspects of Semidefinite Programming

Author : E. de Klerk
Publisher : Springer Science & Business Media
ISBN 13 : 1402005474
Total Pages : 287 pages
Book Rating : 4.4/5 (2 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 2002-03-31 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.

Approximation Algorithms and Semidefinite Programming

Author : Bernd Gärtner
Publisher : Springer Science & Business Media
ISBN 13 : 3642220150
Total Pages : 253 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Approximation Algorithms and Semidefinite Programming by : Bernd Gärtner

Download or read book Approximation Algorithms and Semidefinite Programming written by Bernd Gärtner and published by Springer Science & Business Media. This book was released on 2012-01-10 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Handbook of Semidefinite Programming

Author : Henry Wolkowicz
Publisher : Springer Science & Business Media
ISBN 13 : 1461543819
Total Pages : 660 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Handbook of Semidefinite Programming by : Henry Wolkowicz

Download or read book Handbook of Semidefinite Programming written by Henry Wolkowicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Semidefinite Optimization and Convex Algebraic Geometry

Author : Grigoriy Blekherman
Publisher : SIAM
ISBN 13 : 1611972280
Total Pages : 487 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Semidefinite Optimization and Convex Algebraic Geometry by : Grigoriy Blekherman

Download or read book Semidefinite Optimization and Convex Algebraic Geometry written by Grigoriy Blekherman and published by SIAM. This book was released on 2013-03-21 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.

Handbook on Semidefinite, Conic and Polynomial Optimization

Author : Miguel F. Anjos
Publisher : Springer Science & Business Media
ISBN 13 : 1461407699
Total Pages : 955 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Handbook on Semidefinite, Conic and Polynomial Optimization by : Miguel F. Anjos

Download or read book Handbook on Semidefinite, Conic and Polynomial Optimization written by Miguel F. Anjos and published by Springer Science & Business Media. This book was released on 2011-11-19 with total page 955 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems. Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity. This Handbook on Semidefinite, Conic and Polynomial Optimization provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral students, young graduates, and experienced researchers alike. The Handbook’s thirty-one chapters are organized into four parts: Theory, covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization; Algorithms, documenting the directions of current algorithmic development; Software, providing an overview of the state-of-the-art; Applications, dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.

Recent Advances in Algorithms and Combinatorics

Author : Bruce A. Reed
Publisher : Springer Science & Business Media
ISBN 13 : 0387224440
Total Pages : 357 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Recent Advances in Algorithms and Combinatorics by : Bruce A. Reed

Download or read book Recent Advances in Algorithms and Combinatorics written by Bruce A. Reed and published by Springer Science & Business Media. This book was released on 2006-05-17 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent authors, such as Lovasz, one of the five best combinatorialists in the world; Thematic linking that makes it a coherent collection; Will appeal to a variety of communities, such as mathematics, computer science and operations research

Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization

Author : Levent Tuncel
Publisher : American Mathematical Soc.
ISBN 13 : 0821871854
Total Pages : 233 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization by : Levent Tuncel

Download or read book Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization written by Levent Tuncel and published by American Mathematical Soc.. This book was released on with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Interior Point Algorithms

Author : Yinyu Ye
Publisher : John Wiley & Sons
ISBN 13 : 1118030958
Total Pages : 440 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Interior Point Algorithms by : Yinyu Ye

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.

Low-Rank Semidefinite Programming

Author : Alex Lemon
Publisher : Now Publishers
ISBN 13 : 9781680831368
Total Pages : 180 pages
Book Rating : 4.8/5 (313 download)

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Book Synopsis Low-Rank Semidefinite Programming by : Alex Lemon

Download or read book Low-Rank Semidefinite Programming written by Alex Lemon and published by Now Publishers. This book was released on 2016-05-04 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finding low-rank solutions of semidefinite programs is important in many applications. For example, semidefinite programs that arise as relaxations of polynomial optimization problems are exact relaxations when the semidefinite program has a rank-1 solution. Unfortunately, computing a minimum-rank solution of a semidefinite program is an NP-hard problem. This monograph reviews the theory of low-rank semidefinite programming, presenting theorems that guarantee the existence of a low-rank solution, heuristics for computing low-rank solutions, and algorithms for finding low-rank approximate solutions. It then presents applications of the theory to trust-region problems and signal processing.

Lectures on Modern Convex Optimization

Author : Aharon Ben-Tal
Publisher : SIAM
ISBN 13 : 0898714915
Total Pages : 500 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Lectures on Modern Convex Optimization by : Aharon Ben-Tal

Download or read book Lectures on Modern Convex Optimization written by Aharon Ben-Tal and published by SIAM. This book was released on 2001-01-01 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.

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.

Interior-point Polynomial Algorithms in Convex Programming

Author : Yurii Nesterov
Publisher : SIAM
ISBN 13 : 9781611970791
Total Pages : 414 pages
Book Rating : 4.9/5 (77 download)

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Book Synopsis Interior-point Polynomial Algorithms in Convex Programming by : Yurii Nesterov

Download or read book Interior-point Polynomial Algorithms in Convex Programming written by Yurii Nesterov and published by SIAM. This book was released on 1994-01-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Specialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. A background in linear algebra and mathematical programming is necessary to understand the book. The detailed proofs and lack of "numerical examples" might suggest that the book is of limited value to the reader interested in the practical aspects of convex optimization, but nothing could be further from the truth. An entire chapter is devoted to potential reduction methods precisely because of their great efficiency in practice.

Completely Positive Matrices

Author : Abraham Berman
Publisher : World Scientific
ISBN 13 : 9789812795212
Total Pages : 222 pages
Book Rating : 4.7/5 (952 download)

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Book Synopsis Completely Positive Matrices by : Abraham Berman

Download or read book Completely Positive Matrices written by Abraham Berman and published by World Scientific. This book was released on 2003 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: A real matrix is positive semidefinite if it can be decomposed as A = BBOC . In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A = BBOC is known as the cp- rank of A . This invaluable book focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp- rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined. Contents: Preliminaries: Matrix Theoretic Background; Positive Semidefinite Matrices; Nonnegative Matrices and M -Matrices; Schur Complements; Graphs; Convex Cones; The PSD Completion Problem; Complete Positivity: Definition and Basic Properties; Cones of Completely Positive Matrices; Small Matrices; Complete Positivity and the Comparison Matrix; Completely Positive Graphs; Completely Positive Matrices Whose Graphs are Not Completely Positive; Square Factorizations; Functions of Completely Positive Matrices; The CP Completion Problem; CP Rank: Definition and Basic Results; Completely Positive Matrices of a Given Rank; Completely Positive Matrices of a Given Order; When is the CP-Rank Equal to the Rank?. Readership: Upper level undergraduates, graduate students, academics and researchers interested in matrix theory."

Concise Encyclopedia of Coding Theory

Author : W. Cary Huffman
Publisher : CRC Press
ISBN 13 : 1351375105
Total Pages : 998 pages
Book Rating : 4.3/5 (513 download)

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Book Synopsis Concise Encyclopedia of Coding Theory by : W. Cary Huffman

Download or read book Concise Encyclopedia of Coding Theory written by W. Cary Huffman and published by CRC Press. This book was released on 2021-03-26 with total page 998 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research

Communications, Computation, Control, and Signal Processing

Author : Arogyaswami Paulraj
Publisher : Springer Science & Business Media
ISBN 13 : 1461562813
Total Pages : 572 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Communications, Computation, Control, and Signal Processing by : Arogyaswami Paulraj

Download or read book Communications, Computation, Control, and Signal Processing written by Arogyaswami Paulraj and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: A. Paulraj*, V. Roychowdhury**, and C. Schaper* * Dept. of Electrical Engineering, Stanford University ** Dept. of Electrical Engineering, UCLA Innumerable conferences are held around the world on the subjects of commu nications, computation, control and signal processing, and on their numerous subdisciplines. Therefore one might not envision a coherent conference encom passing all these areas. However, such an event did take place June 22-26, 1995, at an international symposium held at Stanford University to celebrate Professor Thomas Kailath's sixtieth birthday and to honor the notable con tributions made by him and his students and associates. The depth of these contributions was evident from the participation of so many leading figures in each of these fields. Over the five days of the meeting, there were about 200 at tendees, from eighteen countries, more than twenty government and industrial organizations, and various engineering, mathematics and statistics faculties at nearly 50 different academic institutions. They came not only to celebrate but also to learn and to ponder the threads and the connections that Professor Kailath has discovered and woven among so many apparently disparate areas. The organizers received many comments about the richness of the occasion. A distinguished academic wrote of the conference being "the single most rewarding professional event of my life. " The program is summarized in Table 1. 1; a letter of reflections by Dr. C. Rohrs appears a little later.

Chordal Graphs and Semidefinite Optimization

Author : Lieven Vandenberghe
Publisher : Foundations and Trends (R) in Optimization
ISBN 13 : 9781680830385
Total Pages : 216 pages
Book Rating : 4.8/5 (33 download)

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Book Synopsis Chordal Graphs and Semidefinite Optimization by : Lieven Vandenberghe

Download or read book Chordal Graphs and Semidefinite Optimization written by Lieven Vandenberghe and published by Foundations and Trends (R) in Optimization. This book was released on 2015-04-30 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the theory and applications of chordal graphs, with an emphasis on algorithms developed in the literature on sparse Cholesky factorization. It shows how these techniques can be applied in algorithms for sparse semidefinite optimization, and points out the connections with related topics outside semidefinite optimization.