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Interior Point Methods for Linear Optimization

2006-02-08 Mathematics
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Release : 2006-02-08
Genre : Mathematics
Kind : eBook
Book Rating : 799/5 ( reviews)

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Book Synopsis Interior Point Methods for Linear Optimization by : Cornelis Roos

Download or read book Interior Point Methods for Linear Optimization written by Cornelis Roos. This book was released on 2006-02-08. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Theory and Algorithms for Linear Optimization

1997-03-04 Mathematics
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Release : 1997-03-04
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Theory and Algorithms for Linear Optimization by : Cornelis Roos

Download or read book Theory and Algorithms for Linear Optimization written by Cornelis Roos. This book was released on 1997-03-04. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Primal-dual Interior-Point Methods

1997-01-01 Interior-point methods
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Release : 1997-01-01
Genre : Interior-point methods
Kind : eBook
Book Rating : 453/5 ( reviews)

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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. This book was released on 1997-01-01. 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 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 Techniques in Optimization

2013-03-14 Mathematics
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Release : 2013-03-14
Genre : Mathematics
Kind : eBook
Book Rating : 619/5 ( reviews)

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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. This book was released on 2013-03-14. 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.

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