Interior-point Polynomial Algorithms in Convex Programming

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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.

Interior Point Approach to Linear, Quadratic and Convex Programming

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9401111340
Total Pages : 214 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Interior Point Approach to Linear, Quadratic and Convex Programming by : D. den Hertog

Download or read book Interior Point Approach to Linear, Quadratic and Convex Programming written by D. den Hertog and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An O(n3L) Interior Point Algorithm for Convex Quadratic Programming

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Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis An O(n3L) Interior Point Algorithm for Convex Quadratic Programming by : R. C. Monteiro

Download or read book An O(n3L) Interior Point Algorithm for Convex Quadratic Programming written by R. C. Monteiro and published by . This book was released on 1987 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors describe a primal-dual interior point algorithm for convex quadratic programming problems which requires a total of O(cu n L) arithmetic operations. Each iteration updates a penalty parameter and finds an approximate Newton's direction associated with the Kuhn-Tucker system of equations which characterizes a solution of the logarithm barrier function problem. This direction is then used to find the next iterate. The algorithm is based on the path following idea. The total number of iterations is shown to be of the order of O (square root of n L). Keywords: Interior-point methods; Convex quadratic programming; Karmarkar's algorithm; Polynomial-time algorithms; Barrier function; Path following. (Author).

A Simple, Quadratically Convergent Interior Point Algorithm for Linear Programming and Convex Quadratic Programming

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Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (897 download)

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Book Synopsis A Simple, Quadratically Convergent Interior Point Algorithm for Linear Programming and Convex Quadratic Programming by : A. L. Tits

Download or read book A Simple, Quadratically Convergent Interior Point Algorithm for Linear Programming and Convex Quadratic Programming written by A. L. Tits and published by . This book was released on 1993 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Interior Point Techniques in Optimization

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Publisher : Springer Science & Business Media
ISBN 13 : 1475755619
Total Pages : 285 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Interior Point Techniques in Optimization by : B. Jansen

Download or read book Interior Point Techniques in Optimization written by B. Jansen and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Author :
Publisher : SIAM
ISBN 13 : 9780898718812
Total Pages : 124 pages
Book Rating : 4.7/5 (188 download)

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Book Synopsis A Mathematical View of Interior-point Methods in Convex Optimization by : James Renegar

Download or read book A Mathematical View of Interior-point Methods in Convex Optimization written by James Renegar and published by SIAM. This book was released on 2001-01-01 with total page 124 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.

Interior Point Algorithms

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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.

An Introduction to Interior Point Algorithms for Linear and Convex Quadratic Programming

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Publisher :
ISBN 13 :
Total Pages : 57 pages
Book Rating : 4.:/5 (662 download)

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Book Synopsis An Introduction to Interior Point Algorithms for Linear and Convex Quadratic Programming by : B. Jansen

Download or read book An Introduction to Interior Point Algorithms for Linear and Convex Quadratic Programming written by B. Jansen and published by . This book was released on 1992 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Arc-Search Techniques for Interior-Point Methods

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Publisher : CRC Press
ISBN 13 : 1000220338
Total Pages : 495 pages
Book Rating : 4.0/5 (2 download)

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Book Synopsis Arc-Search Techniques for Interior-Point Methods by : Yaguang Yang

Download or read book Arc-Search Techniques for Interior-Point Methods written by Yaguang Yang and published by CRC Press. This book was released on 2020-11-26 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Regularized Active-Set method For Sparse Convex Quadratic Programming

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Author :
Publisher : Stanford University
ISBN 13 :
Total Pages : 128 pages
Book Rating : 4./5 ( download)

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Book Synopsis A Regularized Active-Set method For Sparse Convex Quadratic Programming by :

Download or read book A Regularized Active-Set method For Sparse Convex Quadratic Programming written by and published by Stanford University. This book was released on with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on Modern Convex Optimization

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Publisher : SIAM
ISBN 13 : 9780898718829
Total Pages : 504 pages
Book Rating : 4.7/5 (188 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 504 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.

Practical Aspects of an Interior-point Method for Convex Programming

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Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Practical Aspects of an Interior-point Method for Convex Programming by : Stanford University. Department of Operations Research. Systems Optimization Laboratory

Download or read book Practical Aspects of an Interior-point Method for Convex Programming written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and published by . This book was released on 1991 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Interior-point Algorithm for Indefinite Quadratic Programming

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Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (242 download)

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Book Synopsis An Interior-point Algorithm for Indefinite Quadratic Programming by : Chi-Guen Han

Download or read book An Interior-point Algorithm for Indefinite Quadratic Programming written by Chi-Guen Han and published by . This book was released on 1990 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "In this paper, we discuss theoretical and computational aspects of an interior-point algorithm for indefinite quadratic programming problems with box constraints. The algorithm finds a stationary point that satisfies the Kuhn-Tucker conditions, by successively solving indefinite quadratic problems with an ellipsoid constraint. In addition, we present a sufficient condition for a local minimum to be global, and we use this result to generate test problems with a known global solution. The proposed algorithm has been implemented on an IBM 3090 computer and tested on a variety of dense test problems, including problems with a known global optimum."

Interior Point Methods in Mathematical Programming

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Publisher :
ISBN 13 :
Total Pages : 598 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Interior Point Methods in Mathematical Programming by : Kurt M. Anstreicher

Download or read book Interior Point Methods in Mathematical Programming written by Kurt M. Anstreicher and published by . This book was released on 1996 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Study of Projective Algorithms for Linear and Convex Quadratic Programming

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Publisher :
ISBN 13 :
Total Pages : 244 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis A Study of Projective Algorithms for Linear and Convex Quadratic Programming by : Yufei Wang

Download or read book A Study of Projective Algorithms for Linear and Convex Quadratic Programming written by Yufei Wang and published by . This book was released on 1992 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Interior Point Approach to Linear, Quadratic and Convex Programming

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Author :
Publisher :
ISBN 13 :
Total Pages : 207 pages
Book Rating : 4.:/5 (636 download)

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Book Synopsis Interior Point Approach to Linear, Quadratic and Convex Programming by : Dirk den Hertog (Mathematician, Netherlands)

Download or read book Interior Point Approach to Linear, Quadratic and Convex Programming written by Dirk den Hertog (Mathematician, Netherlands) and published by . This book was released on 1992 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt:

polynomially bounded ellipsoid algorithms for convex quadratic programming

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Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis polynomially bounded ellipsoid algorithms for convex quadratic programming by : sung j. chung, katta g. murty

Download or read book polynomially bounded ellipsoid algorithms for convex quadratic programming written by sung j. chung, katta g. murty and published by . This book was released on 1980 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: