Topics In Semidefinite And Interior Point Methods

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Topics in Semidefinite and Interior-Point Methods

Panos M. Pardalos,Henry Wolkowicz
Topics in Semidefinite and Interior Point Methods Book PDF

Author : Panos M. Pardalos,Henry Wolkowicz
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 51,9 Mb
Release : 1998
Category : Interior-point methods
ISBN : 9780821808252

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Topics in Semidefinite and Interior-Point Methods by Panos M. Pardalos,Henry Wolkowicz Pdf

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.

Topics in Semidefinite and Interior-Point Methods

Panos M. Pardalos and Henry Wolkowicz
Topics in Semidefinite and Interior Point Methods Book PDF

Author : Panos M. Pardalos and Henry Wolkowicz
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 42,8 Mb
Release : 2024-06-16
Category : Interior-point methods
ISBN : 0821871250

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Topics in Semidefinite and Interior-Point Methods by Panos M. Pardalos and Henry Wolkowicz Pdf

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.

Aspects of Semidefinite Programming

E. de Klerk
Aspects of Semidefinite Programming Book PDF

Author : E. de Klerk
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 43,7 Mb
Release : 2006-04-18
Category : Computers
ISBN : 9780306478192

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Aspects of Semidefinite Programming by E. de Klerk Pdf

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.

Interior Point Techniques in Optimization

B. Jansen
Interior Point Techniques in Optimization Book PDF

Author : B. Jansen
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 52,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475755619

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Interior Point Techniques in Optimization by B. Jansen Pdf

Operations research and mathematical programming would not be as advanced today without the many advances in interior point methods during the last decade. These methods can now solve very efficiently and robustly large scale linear, nonlinear and combinatorial optimization problems that arise in various practical applications. The main ideas underlying interior point methods have influenced virtually all areas of mathematical programming including: analyzing and solving linear and nonlinear programming problems, sensitivity analysis, complexity analysis, the analysis of Newton's method, decomposition methods, polynomial approximation for combinatorial problems etc. This book covers the implications of interior techniques for the entire field of mathematical programming, bringing together many results in a uniform and coherent way. For the topics mentioned above the book provides theoretical as well as computational results, explains the intuition behind the main ideas, gives examples as well as proofs, and contains an extensive up-to-date bibliography. Audience: The book is intended for students, researchers and practitioners with a background in operations research, mathematics, mathematical programming, or statistics.

A Mathematical View of Interior-point Methods in Convex Optimization

James Renegar
A Mathematical View of Interior point Methods in Convex Optimization Book PDF

Author : James Renegar
Publisher : SIAM
Page : 124 pages
File Size : 46,6 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 0898718813

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A Mathematical View of Interior-point Methods in Convex Optimization by James Renegar Pdf

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.

Interior Point Methods of Mathematical Programming

Tamás Terlaky
Interior Point Methods of Mathematical Programming Book PDF

Author : Tamás Terlaky
Publisher : Springer Science & Business Media
Page : 544 pages
File Size : 42,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461334491

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Interior Point Methods of Mathematical Programming by Tamás Terlaky Pdf

One has to make everything as simple as possible but, never more simple. Albert Einstein Discovery consists of seeing what every body has seen and thinking what nobody has thought. Albert S. ent_Gyorgy; The primary goal of this book is to provide an introduction to the theory of Interior Point Methods (IPMs) in Mathematical Programming. At the same time, we try to present a quick overview of the impact of extensions of IPMs on smooth nonlinear optimization and to demonstrate the potential of IPMs for solving difficult practical problems. The Simplex Method has dominated the theory and practice of mathematical pro gramming since 1947 when Dantzig discovered it. In the fifties and sixties several attempts were made to develop alternative solution methods. At that time the prin cipal base of interior point methods was also developed, for example in the work of Frisch (1955), Caroll (1961), Huard (1967), Fiacco and McCormick (1968) and Dikin (1967). In 1972 Klee and Minty made explicit that in the worst case some variants of the simplex method may require an exponential amount of work to solve Linear Programming (LP) problems. This was at the time when complexity theory became a topic of great interest. People started to classify mathematical programming prob lems as efficiently (in polynomial time) solvable and as difficult (NP-hard) problems. For a while it remained open whether LP was solvable in polynomial time or not. The break-through resolution ofthis problem was obtained by Khachijan (1989).

Encyclopedia of Optimization

Christodoulos A. Floudas,Panos M. Pardalos
Encyclopedia of Optimization Book PDF

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 4646 pages
File Size : 51,8 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780387747583

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Encyclopedia of Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Self-Regularity

Jiming Peng,Cornelis Roos,Tamás Terlaky
Self Regularity Book PDF

Author : Jiming Peng,Cornelis Roos,Tamás Terlaky
Publisher : Princeton University Press
Page : 208 pages
File Size : 51,6 Mb
Release : 2009-01-10
Category : Mathematics
ISBN : 9781400825134

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Self-Regularity by Jiming Peng,Cornelis Roos,Tamás Terlaky Pdf

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.

Computational Optimization

Jong-Shi Pang
Computational Optimization Book PDF

Author : Jong-Shi Pang
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461551973

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Computational Optimization by Jong-Shi Pang Pdf

Computational Optimization: A Tribute to Olvi Mangasarian serves as an excellent reference, providing insight into some of the most challenging research issues in the field. This collection of papers covers a wide spectrum of computational optimization topics, representing a blend of familiar nonlinear programming topics and such novel paradigms as semidefinite programming and complementarity-constrained nonlinear programs. Many new results are presented in these papers which are bound to inspire further research and generate new avenues for applications. An informal categorization of the papers includes: Algorithmic advances for special classes of constrained optimization problems Analysis of linear and nonlinear programs Algorithmic advances B- stationary points of mathematical programs with equilibrium constraints Applications of optimization Some mathematical topics Systems of nonlinear equations.

Primal-Dual Interior-Point Methods

Stephen J. Wright
Primal Dual Interior Point Methods Book PDF

Author : Stephen J. Wright
Publisher : SIAM
Page : 293 pages
File Size : 52,9 Mb
Release : 1997-01-01
Category : Technology & Engineering
ISBN : 9780898713824

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Primal-Dual Interior-Point Methods by Stephen J. Wright Pdf

Presents the major primal-dual algorithms for linear programming. A thorough, straightforward description of the theoretical properties of these methods.

Handbook of Linear Algebra, Second Edition

Leslie Hogben
Handbook of Linear Algebra Second Edition Book PDF

Author : Leslie Hogben
Publisher : CRC Press
Page : 1906 pages
File Size : 44,8 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9781466507289

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Handbook of Linear Algebra, Second Edition by Leslie Hogben Pdf

With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters. New to the Second Edition Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems More chapters on applications of linear algebra, including epidemiology and quantum error correction New chapter on using the free and open source software system Sage for linear algebra Additional sections in the chapters on sign pattern matrices and applications to geometry Conjectures and open problems in most chapters on advanced topics Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.

Nonlinear Optimization

Immanuel M. Bomze,Vladimir F. Demyanov,Roger Fletcher,Tamás Terlaky
Nonlinear Optimization Book PDF

Author : Immanuel M. Bomze,Vladimir F. Demyanov,Roger Fletcher,Tamás Terlaky
Publisher : Springer
Page : 279 pages
File Size : 42,8 Mb
Release : 2010-03-17
Category : Mathematics
ISBN : 9783642113390

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Nonlinear Optimization by Immanuel M. Bomze,Vladimir F. Demyanov,Roger Fletcher,Tamás Terlaky Pdf

This volume collects the expanded notes of four series of lectures given on the occasion of the CIME course on Nonlinear Optimization held in Cetraro, Italy, from July 1 to 7, 2007. The Nonlinear Optimization problem of main concern here is the problem n of determining a vector of decision variables x ? R that minimizes (ma- n mizes) an objective function f(·): R ? R,when x is restricted to belong n to some feasible setF? R , usually described by a set of equality and - n n m equality constraints: F = {x ? R : h(x)=0,h(·): R ? R ; g(x) ? 0, n p g(·): R ? R }; of course it is intended that at least one of the functions f,h,g is nonlinear. Although the problem canbe stated in verysimpleterms, its solution may result very di?cult due to the analytical properties of the functions involved and/or to the number n,m,p of variables and constraints. On the other hand, the problem has been recognized to be of main relevance in engineering, economics, and other applied sciences, so that a great lot of e?ort has been devoted to develop methods and algorithms able to solve the problem even in its more di?cult and large instances. The lectures have been given by eminent scholars, who contributed to a great extent to the development of Nonlinear Optimization theory, methods and algorithms. Namely, they are: – Professor Immanuel M.

Handbooks in Operations Research and Management Science

K. Aardal,George L. Nemhauser,R. Weismantel
Handbooks in Operations Research and Management Science Book PDF

Author : K. Aardal,George L. Nemhauser,R. Weismantel
Publisher : Elsevier
Page : 620 pages
File Size : 43,7 Mb
Release : 2005-12-08
Category : Business & Economics
ISBN : 0080459218

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Handbooks in Operations Research and Management Science by K. Aardal,George L. Nemhauser,R. Weismantel Pdf

The chapters of this Handbook volume cover nine main topics that are representative of recent theoretical and algorithmic developments in the field. In addition to the nine papers that present the state of the art, there is an article on the early history of the field. The handbook will be a useful reference to experts in the field as well as students and others who want to learn about discrete optimization.

Topics in Operator Theory

Joseph A. Ball,Vladimir Bolotnikov,J. William Helton,Leiba Rodman,Ilya M. Spitkovsky
Topics in Operator Theory Book PDF

Author : Joseph A. Ball,Vladimir Bolotnikov,J. William Helton,Leiba Rodman,Ilya M. Spitkovsky
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 48,8 Mb
Release : 2011-02-09
Category : Mathematics
ISBN : 9783034601580

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Topics in Operator Theory by Joseph A. Ball,Vladimir Bolotnikov,J. William Helton,Leiba Rodman,Ilya M. Spitkovsky Pdf

This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.

Interior-point Polynomial Algorithms in Convex Programming

Yurii Nesterov,Arkadii Nemirovskii
Interior point Polynomial Algorithms in Convex Programming Book PDF

Author : Yurii Nesterov,Arkadii Nemirovskii
Publisher : SIAM
Page : 414 pages
File Size : 54,7 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 1611970792

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Interior-point Polynomial Algorithms in Convex Programming by Yurii Nesterov,Arkadii Nemirovskii Pdf

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.