Implementation Of An Interior Point Cutting Plane Algorithm

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Interior Point Methods of Mathematical Programming

Author : Tamás Terlaky
Publisher : Springer Science & Business Media
ISBN 13 : 1461334497
Total Pages : 544 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Interior Point Methods of Mathematical Programming by : Tamás Terlaky

Download or read book Interior Point Methods of Mathematical Programming written by Tamás Terlaky and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Interior Point Algorithms

Author : Yinyu Ye
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.

Interior-point Polynomial Algorithms in Convex Programming

Author : Yurii Nesterov
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 Techniques in Optimization

Author : B. Jansen
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.

Interior Point Methods in Mathematical Programming

Author : Kurt M. Anstreicher
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:

Handbook of combinatorial optimization. 1

Author : Dingzhu Du
Publisher : Springer Science & Business Media
ISBN 13 : 9780792350187
Total Pages : 808 pages
Book Rating : 4.3/5 (51 download)

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Book Synopsis Handbook of combinatorial optimization. 1 by : Dingzhu Du

Download or read book Handbook of combinatorial optimization. 1 written by Dingzhu Du and published by Springer Science & Business Media. This book was released on 1998 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of a multi-volume set, which deals with several algorithmic approaches for discrete problems as well as many combinatorial problems. It is addressed to researchers in discrete optimization, and to all scientists who use combinatorial optimization methods to model and solve problems.

Handbook of Combinatorial Optimization

Author : Ding-Zhu Du
Publisher : Springer Science & Business Media
ISBN 13 : 1461303036
Total Pages : 2410 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Handbook of Combinatorial Optimization by : Ding-Zhu Du

Download or read book Handbook of Combinatorial Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 2410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial (or discrete) optimization is one of the most active fields in the interface of operations research, computer science, and applied math ematics. Combinatorial optimization problems arise in various applications, including communications network design, VLSI design, machine vision, air line crew scheduling, corporate planning, computer-aided design and man ufacturing, database query design, cellular telephone frequency assignment, constraint directed reasoning, and computational biology. Furthermore, combinatorial optimization problems occur in many diverse areas such as linear and integer programming, graph theory, artificial intelligence, and number theory. All these problems, when formulated mathematically as the minimization or maximization of a certain function defined on some domain, have a commonality of discreteness. Historically, combinatorial optimization starts with linear programming. Linear programming has an entire range of important applications including production planning and distribution, personnel assignment, finance, alloca tion of economic resources, circuit simulation, and control systems. Leonid Kantorovich and Tjalling Koopmans received the Nobel Prize (1975) for their work on the optimal allocation of resources. Two important discover ies, the ellipsoid method (1979) and interior point approaches (1984) both provide polynomial time algorithms for linear programming. These algo rithms have had a profound effect in combinatorial optimization. Many polynomial-time solvable combinatorial optimization problems are special cases of linear programming (e.g. matching and maximum flow). In addi tion, linear programming relaxations are often the basis for many approxi mation algorithms for solving NP-hard problems (e.g. dual heuristics).

High Performance Optimization

Author : Hans Frenk
Publisher : Springer Science & Business Media
ISBN 13 : 1475732163
Total Pages : 485 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis High Performance Optimization by : Hans Frenk

Download or read book High Performance Optimization written by Hans Frenk and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a long time the techniques of solving linear optimization (LP) problems improved only marginally. Fifteen years ago, however, a revolutionary discovery changed everything. A new `golden age' for optimization started, which is continuing up to the current time. What is the cause of the excitement? Techniques of linear programming formed previously an isolated body of knowledge. Then suddenly a tunnel was built linking it with a rich and promising land, part of which was already cultivated, part of which was completely unexplored. These revolutionary new techniques are now applied to solve conic linear problems. This makes it possible to model and solve large classes of essentially nonlinear optimization problems as efficiently as LP problems. This volume gives an overview of the latest developments of such `High Performance Optimization Techniques'. The first part is a thorough treatment of interior point methods for semidefinite programming problems. The second part reviews today's most exciting research topics and results in the area of convex optimization. Audience: This volume is for graduate students and researchers who are interested in modern optimization techniques.

Interior Point Methods for Linear Optimization

Author : Cornelis Roos
Publisher : Springer Science & Business Media
ISBN 13 : 0387263799
Total Pages : 501 pages
Book Rating : 4.3/5 (872 download)

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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 and published by Springer Science & Business Media. This book was released on 2006-02-08 with total page 501 pages. 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.

Linear Programming 1

Author : George B. Dantzig
Publisher : Springer Science & Business Media
ISBN 13 : 0387948333
Total Pages : 462 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Linear Programming 1 by : George B. Dantzig

Download or read book Linear Programming 1 written by George B. Dantzig and published by Springer Science & Business Media. This book was released on 1997-01-27 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Encompassing all the major topics students will encounter in courses on the subject, the authors teach both the underlying mathematical foundations and how these ideas are implemented in practice. They illustrate all the concepts with both worked examples and plenty of exercises, and, in addition, provide software so that students can try out numerical methods and so hone their skills in interpreting the results. As a result, this will make an ideal textbook for all those coming to the subject for the first time. Authors' note: A problem recently found with the software is due to a bug in Formula One, the third party commercial software package that was used for the development of the interface. It occurs when the date, currency, etc. format is set to a non-United States version. Please try setting your computer date/currency option to the United States option . The new version of Formula One, when ready, will be posted on WWW.

Handbook on Semidefinite, Conic and Polynomial Optimization

Author : Miguel F. Anjos
Publisher : Springer Science & Business Media
ISBN 13 : 1461407699
Total Pages : 955 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Handbook on Semidefinite, Conic and Polynomial Optimization by : Miguel F. Anjos

Download or read book Handbook on Semidefinite, Conic and Polynomial Optimization written by Miguel F. Anjos and published by Springer Science & Business Media. This book was released on 2011-11-19 with total page 955 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems. Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity. This Handbook on Semidefinite, Conic and Polynomial Optimization provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral students, young graduates, and experienced researchers alike. The Handbook’s thirty-one chapters are organized into four parts: Theory, covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization; Algorithms, documenting the directions of current algorithmic development; Software, providing an overview of the state-of-the-art; Applications, dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.

Handbook of Optimization in Telecommunications

Author : Mauricio G.C. Resende
Publisher : Springer Science & Business Media
ISBN 13 : 0387301658
Total Pages : 1120 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Handbook of Optimization in Telecommunications by : Mauricio G.C. Resende

Download or read book Handbook of Optimization in Telecommunications written by Mauricio G.C. Resende and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 1120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive handbook brings together experts who use optimization to solve problems that arise in telecommunications. It is the first book to cover in detail the field of optimization in telecommunications. Recent optimization developments that are frequently applied to telecommunications are covered. The spectrum of topics covered includes planning and design of telecommunication networks, routing, network protection, grooming, restoration, wireless communications, network location and assignment problems, Internet protocol, World Wide Web, and stochastic issues in telecommunications. The book’s objective is to provide a reference tool for the increasing number of scientists and engineers in telecommunications who depend upon optimization.

Progress in Mathematical Programming

Author : Nimrod Megiddo
Publisher : Springer Science & Business Media
ISBN 13 : 1461396174
Total Pages : 164 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Progress in Mathematical Programming by : Nimrod Megiddo

Download or read book Progress in Mathematical Programming written by Nimrod Megiddo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Optimization Methods and Applications

Author : Xiao-qi Yang
Publisher : Springer Science & Business Media
ISBN 13 : 147573333X
Total Pages : 439 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Optimization Methods and Applications by : Xiao-qi Yang

Download or read book Optimization Methods and Applications written by Xiao-qi Yang and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited book is dedicated to Professor N. U. Ahmed, a leading scholar and a renowned researcher in optimal control and optimization on the occasion of his retirement from the Department of Electrical Engineering at University of Ottawa in 1999. The contributions of this volume are in the areas of optimal control, non linear optimization and optimization applications. They are mainly the im proved and expanded versions of the papers selected from those presented in two special sessions of two international conferences. The first special session is Optimization Methods, which was organized by K. L. Teo and X. Q. Yang for the International Conference on Optimization and Variational Inequality, the City University of Hong Kong, Hong Kong, 1998. The other one is Optimal Control, which was organized byK. ~Teo and L. Caccetta for the Dynamic Control Congress, Ottawa, 1999. This volume is divided into three parts: Optimal Control; Optimization Methods; and Applications. The Optimal Control part is concerned with com putational methods, modeling and nonlinear systems. Three computational methods for solving optimal control problems are presented: (i) a regularization method for computing ill-conditioned optimal control problems, (ii) penalty function methods that appropriately handle final state equality constraints, and (iii) a multilevel optimization approach for the numerical solution of opti mal control problems. In the fourth paper, the worst-case optimal regulation involving linear time varying systems is formulated as a minimax optimal con trol problem.

Column Generation

Author : Guy Desaulniers
Publisher : Springer Science & Business Media
ISBN 13 : 0387254862
Total Pages : 369 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Column Generation by : Guy Desaulniers

Download or read book Column Generation written by Guy Desaulniers and published by Springer Science & Business Media. This book was released on 2006-03-20 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Column Generation is an insightful overview of the state of the art in integer programming column generation and its many applications. The volume begins with "A Primer in Column Generation" which outlines the theory and ideas necessary to solve large-scale practical problems, illustrated with a variety of examples. Other chapters follow this introduction on "Shortest Path Problems with Resource Constraints," "Vehicle Routing Problem with Time Window," "Branch-and-Price Heuristics," "Cutting Stock Problems," each dealing with methodological aspects of the field. Three chapters deal with transportation applications: "Large-scale Models in the Airline Industry," "Robust Inventory Ship Routing by Column Generation," and "Ship Scheduling with Recurring Visits and Visit Separation Requirements." Production is the focus of another three chapters: "Combining Column Generation and Lagrangian Relaxation," "Dantzig-Wolfe Decomposition for Job Shop Scheduling," and "Applying Column Generation to Machine Scheduling." The final chapter by François Vanderbeck, "Implementing Mixed Integer Column Generation," reviews how to set-up the Dantzig-Wolfe reformulation, adapt standard MIP techniques to the column generation context (branching, preprocessing, primal heuristics), and deal with specific column generation issues (initialization, stabilization, column management strategies).

Combinatorial Optimization

Author : William Cook
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870662
Total Pages : 464 pages
Book Rating : 4.8/5 (76 download)

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Book Synopsis Combinatorial Optimization by : William Cook

Download or read book Combinatorial Optimization written by William Cook and published by American Mathematical Soc.. This book was released on 1995-01-01 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a carefully refereed collection of invited survey articles written by outstanding researchers. Aimed at researchers in discrete mathematics, operations research, and the theory of computing, this book offers an in-depth look at many topics not treated in textbooks.

Interior Point Approach to Linear, Quadratic and Convex Programming

Author : D. den Hertog
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.