Interior Point Approach To Linear Quadratic And Convex Programming

Interior Point Approach To Linear Quadratic And Convex Programming Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Interior Point Approach To Linear Quadratic And Convex Programming book. This book definitely worth reading, it is an incredibly well-written.

Interior Point Approach to Linear, Quadratic and Convex Programming

D. den Hertog
Interior Point Approach to Linear Quadratic and Convex Programming Book PDF

Author : D. den Hertog
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401111348

Get Book

Interior Point Approach to Linear, Quadratic and Convex Programming by D. den Hertog Pdf

This book describes the rapidly developing field of interior point methods (IPMs). An extensive analysis is given of path-following methods for linear programming, quadratic programming and convex programming. These methods, which form a subclass of interior point methods, follow the central path, which is an analytic curve defined by the problem. Relatively simple and elegant proofs for polynomiality are given. The theory is illustrated using several explicit examples. Moreover, an overview of other classes of IPMs is given. It is shown that all these methods rely on the same notion as the path-following methods: all these methods use the central path implicitly or explicitly as a reference path to go to the optimum. For specialists in IPMs as well as those seeking an introduction to IPMs. The book is accessible to any mathematician with basic mathematical programming knowledge.

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 : 51,6 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 1611970792

Get Book

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.

A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems

Masakazu Kojima,N. Megiddo,T. Noma,Akiko Yoshise
A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems Book PDF

Author : Masakazu Kojima,N. Megiddo,T. Noma,Akiko Yoshise
Publisher : Springer Science & Business Media
Page : 124 pages
File Size : 42,6 Mb
Release : 1991-09-25
Category : Language Arts & Disciplines
ISBN : 3540545093

Get Book

A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems by Masakazu Kojima,N. Megiddo,T. Noma,Akiko Yoshise Pdf

Following Karmarkar's 1984 linear programming algorithm, numerous interior-point algorithms have been proposed for various mathematical programming problems such as linear programming, convex quadratic programming and convex programming in general. This monograph presents a study of interior-point algorithms for the linear complementarity problem (LCP) which is known as a mathematical model for primal-dual pairs of linear programs and convex quadratic programs. A large family of potential reduction algorithms is presented in a unified way for the class of LCPs where the underlying matrix has nonnegative principal minors (P0-matrix). This class includes various important subclasses such as positive semi-definite matrices, P-matrices, P*-matrices introduced in this monograph, and column sufficient matrices. The family contains not only the usual potential reduction algorithms but also path following algorithms and a damped Newton method for the LCP. The main topics are global convergence, global linear convergence, and the polynomial-time convergence of potential reduction algorithms included in the family.

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 : 43,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461334491

Get Book

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).

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 : 53,7 Mb
Release : 1997-01-01
Category : Technology & Engineering
ISBN : 9780898713824

Get Book

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.

Interior Point Methods for Linear Optimization

Cornelis Roos,Tamás Terlaky,J.-Ph. Vial
Interior Point Methods for Linear Optimization Book PDF

Author : Cornelis Roos,Tamás Terlaky,J.-Ph. Vial
Publisher : Springer Science & Business Media
Page : 501 pages
File Size : 46,7 Mb
Release : 2006-02-08
Category : Mathematics
ISBN : 9780387263793

Get Book

Interior Point Methods for Linear Optimization by Cornelis Roos,Tamás Terlaky,J.-Ph. Vial Pdf

The era of interior point methods (IPMs) was initiated by N. Karmarkar’s 1984 paper, which triggered turbulent research and reshaped almost all areas of optimization theory and computational practice. This book offers comprehensive coverage of IPMs. It details the main results of more than a decade of IPM research. Numerous exercises are provided to aid in understanding the material.

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 : 52,7 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 0898718813

Get Book

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.

Convex Optimization

Stephen Boyd,Lieven Vandenberghe
Convex Optimization Book PDF

Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 744 pages
File Size : 54,9 Mb
Release : 2004-03-08
Category : Mathematics
ISBN : 9781107394001

Get Book

Convex Optimization by Stephen Boyd,Lieven Vandenberghe Pdf

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Theory and Algorithms for Linear Optimization

Cornelis Roos,T. Terlaky,J.-Ph. Vial
Theory and Algorithms for Linear Optimization Book PDF

Author : Cornelis Roos,T. Terlaky,J.-Ph. Vial
Publisher : Unknown
Page : 520 pages
File Size : 48,6 Mb
Release : 1997-03-04
Category : Mathematics
ISBN : STANFORD:36105019761993

Get Book

Theory and Algorithms for Linear Optimization by Cornelis Roos,T. Terlaky,J.-Ph. Vial Pdf

The approach to LO in this book is new in many aspects. In particular the IPM based development of duality theory is surprisingly elegant. The algorithmic parts of the book contain a complete discussion of many algorithmic variants, including predictor-corrector methods, partial updating, higher order methods and sensitivity and parametric analysis.

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 : 54,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475755619

Get Book

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.

Arc-Search Techniques for Interior-Point Methods

Yaguang Yang
Arc Search Techniques for Interior Point Methods Book PDF

Author : Yaguang Yang
Publisher : CRC Press
Page : 306 pages
File Size : 52,9 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9781000220131

Get Book

Arc-Search Techniques for Interior-Point Methods by Yaguang Yang Pdf

This book discusses an important area of numerical optimization, called interior-point method. This topic has been popular since the 1980s when people gradually realized that all simplex algorithms were not convergent in polynomial time and many interior-point algorithms could be proved to converge in polynomial time. However, for a long time, there was a noticeable gap between theoretical polynomial bounds of the interior-point algorithms and efficiency of these algorithms. Strategies that were important to the computational efficiency became barriers in the proof of good polynomial bounds. The more the strategies were used in algorithms, the worse the polynomial bounds became. To further exacerbate the problem, Mehrotra's predictor-corrector (MPC) algorithm (the most popular and efficient interior-point algorithm until recently) uses all good strategies and fails to prove the convergence. Therefore, MPC does not have polynomiality, a critical issue with the simplex method. This book discusses recent developments that resolves the dilemma. It has three major parts. The first, including Chapters 1, 2, 3, and 4, presents some of the most important algorithms during the development of the interior-point method around the 1990s, most of them are widely known. The main purpose of this part is to explain the dilemma described above by analyzing these algorithms' polynomial bounds and summarizing the computational experience associated with them. The second part, including Chapters 5, 6, 7, and 8, describes how to solve the dilemma step-by-step using arc-search techniques. At the end of this part, a very efficient algorithm with the lowest polynomial bound is presented. The last part, including Chapters 9, 10, 11, and 12, extends arc-search techniques to some more general problems, such as convex quadratic programming, linear complementarity problem, and semi-definite programming.

Interior Point Algorithms

Yinyu Ye
Interior Point Algorithms Book PDF

Author : Yinyu Ye
Publisher : John Wiley & Sons
Page : 440 pages
File Size : 40,6 Mb
Release : 2011-10-11
Category : Mathematics
ISBN : 9781118030950

Get Book

Interior Point Algorithms by Yinyu Ye Pdf

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.

Lectures on Modern Convex Optimization

Aharon Ben-Tal,Arkadi Nemirovski
Lectures on Modern Convex Optimization Book PDF

Author : Aharon Ben-Tal,Arkadi Nemirovski
Publisher : SIAM
Page : 500 pages
File Size : 45,7 Mb
Release : 2001-01-01
Category : Technology & Engineering
ISBN : 9780898714913

Get Book

Lectures on Modern Convex Optimization by Aharon Ben-Tal,Arkadi Nemirovski 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.

Encyclopedia of Operations Research and Management Science

Saul I. Gass,Carl M. Harris
Encyclopedia of Operations Research and Management Science Book PDF

Author : Saul I. Gass,Carl M. Harris
Publisher : Springer Science & Business Media
Page : 969 pages
File Size : 42,8 Mb
Release : 2001
Category : Management science
ISBN : 9780792378273

Get Book

Encyclopedia of Operations Research and Management Science by Saul I. Gass,Carl M. Harris Pdf

Audience: Anyone concerned with the science, techniques and ideas of how decisions are made."--BOOK JACKET.

Progress in Mathematical Programming

Nimrod Megiddo
Progress in Mathematical Programming Book PDF

Author : Nimrod Megiddo
Publisher : Springer Science & Business Media
Page : 164 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461396178

Get Book

Progress in Mathematical Programming by Nimrod Megiddo Pdf

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."