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Large Step Path Following Algorithms For Linear Programming
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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.
Book Synopsis Linear Programming: Mathematics, Theory and Algorithms by : M.J. Panik
Download or read book Linear Programming: Mathematics, Theory and Algorithms written by M.J. Panik and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.
Book Synopsis Mathematical Developments Arising from Linear Programming by : Jeffrey C. Lagarias
Download or read book Mathematical Developments Arising from Linear Programming written by Jeffrey C. Lagarias and published by American Mathematical Soc.. This book was released on 1990 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been much recent work in linear and non-linear programming centred on understanding and extending the ideas underlying Karmarkar's interior-point linear programming algorithm. This volume is the result of an AMS conference on mathematical developments arising from linear programming.
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.
Book Synopsis Large Scale Linear and Integer Optimization: A Unified Approach by : Richard Kipp Martin
Download or read book Large Scale Linear and Integer Optimization: A Unified Approach written by Richard Kipp Martin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook about linear and integer linear optimization. There is a growing need in industries such as airline, trucking, and financial engineering to solve very large linear and integer linear optimization problems. Building these models requires uniquely trained individuals. Not only must they have a thorough understanding of the theory behind mathematical programming, they must have substantial knowledge of how to solve very large models in today's computing environment. The major goal of the book is to develop the theory of linear and integer linear optimization in a unified manner and then demonstrate how to use this theory in a modern computing environment to solve very large real world problems. After presenting introductory material in Part I, Part II of this book is de voted to the theory of linear and integer linear optimization. This theory is developed using two simple, but unifying ideas: projection and inverse projec tion. Through projection we take a system of linear inequalities and replace some of the variables with additional linear inequalities. Inverse projection, the dual of this process, involves replacing linear inequalities with additional variables. Fundamental results such as weak and strong duality, theorems of the alternative, complementary slackness, sensitivity analysis, finite basis the orems, etc. are all explained using projection or inverse projection. Indeed, a unique feature of this book is that these fundamental results are developed and explained before the simplex and interior point algorithms are presented.
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.
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.
Book Synopsis Topics in Semidefinite and Interior-Point Methods by : Panos M. Pardalos
Download or read book Topics in Semidefinite and Interior-Point Methods written by Panos M. Pardalos and published by American Mathematical Soc.. This book was released on 1998 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents refereed papers presented at the workshop Semidefinite Programming and Interior-Point Approaches for Combinatorial Problems: held at The Fields Institute in May 1996. Semidefinite programming (SDP) is a generalization of linear programming (LP) in that the non-negativity constraints on the variables is replaced by a positive semidefinite constraint on matrix variables. Many of the elegant theoretical properties and powerful solution techniques follow through from LP to SDP. In particular, the primal-dual interior-point methods, which are currently so successful for LP, can be used to efficiently solve SDP problems. In addition to the theoretical and algorithmic questions, SDP has found many important applications in combinatorial optimization, control theory and other areas of mathematical programming. The papers in this volume cover a wide spectrum of recent developments in SDP. The volume would be suitable as a textbook for advanced courses in optimization. It is intended for graduate students and researchers in mathematics, computer science, engineering and operations.
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).
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 and published by . This book was released on 1997-03-04 with total page 520 pages. 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.
Author :Joseph-Frédéric Bonnans Publisher :Springer Science & Business Media ISBN 13 :3662050781 Total Pages :421 pages Book Rating :4.6/5 (62 download)
Book Synopsis Numerical Optimization by : Joseph-Frédéric Bonnans
Download or read book Numerical Optimization written by Joseph-Frédéric Bonnans and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. This new edition contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical description when coming to actual implementation.
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.
Author :Christodoulos A. Floudas Publisher :Springer Science & Business Media ISBN 13 :0387747583 Total Pages :4646 pages Book Rating :4.3/5 (877 download)
Book Synopsis Encyclopedia of Optimization by : Christodoulos A. Floudas
Download or read book Encyclopedia of Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2008-09-04 with total page 4646 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
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.
Book Synopsis Optimization: Techniques And Applications (Icota '95) by : G Z Liu
Download or read book Optimization: Techniques And Applications (Icota '95) written by G Z Liu and published by World Scientific. This book was released on 1995-09-01 with total page 1718 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the advent of powerful computers and novel mathematical programming techniques, the multidisciplinary field of optimization has advanced to the stage that quite complicated systems can be addressed. The conference was organized to provide a platform for the exchange of new ideas and information and for identifying needs for future research. The contributions covered both theoretical techniques and a rich variety of case studies to which optimization can be usefully applied.
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."
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 and published by SIAM. This book was released on 1997-01-01 with total page 309 pages. 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.
