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Interior Point Approach to Linear, Quadratic and Convex Programming

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 340/5 ( reviews)

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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. This book was released on 2012-12-06. 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.

Interior-point Polynomial Algorithms in Convex Programming

1994-01-01 Mathematics
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Release : 1994-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 791/5 ( reviews)

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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. This book was released on 1994-01-01. 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

1992
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Release : 1992
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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). This book was released on 1992. Available in PDF, EPUB and Kindle. Book excerpt:

Interior Point Approach to Linear, Quadratic and Convex Programming

1992
Download Interior Point Approach to Linear, Quadratic and Convex Programming PDF Online Free

Author :
Release : 1992
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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

Download or read book Interior Point Approach to Linear, Quadratic and Convex Programming written by Dirk den Hertog. This book was released on 1992. Available in PDF, EPUB and Kindle. Book excerpt:

A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems

1991-09-25 Language Arts & Disciplines
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Release : 1991-09-25
Genre : Language Arts & Disciplines
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Book Rating : 095/5 ( reviews)

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Book Synopsis A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems by : Masakazu Kojima

Download or read book A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems written by Masakazu Kojima. This book was released on 1991-09-25. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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