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Author : Levent Tuncel
Publisher : Unknown
Page : 64 pages
File Size : 47,5 Mb
Release : 1992
Category : Electronic
ISBN : CORNELL:31924063436343
Author : Stephen J. Wright
Publisher : SIAM
Page : 293 pages
File Size : 43,9 Mb
Release : 1997-01-01
Category : Technology & Engineering
ISBN : 9780898713824
Presents the major primal-dual algorithms for linear programming. A thorough, straightforward description of the theoretical properties of these methods.
Author : Yaguang Yang
Publisher : CRC Press
Page : 495 pages
File Size : 50,9 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9781000220339
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.
Author : Levent Tuncel
Publisher : Unknown
Page : 274 pages
File Size : 40,8 Mb
Release : 1993
Category : Electronic
ISBN : CORNELL:31924068312960
Author : B. Jansen
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 53,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475755619
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.
Author : Bao-Liang Lu
Publisher : Springer Science & Business Media
Page : 787 pages
File Size : 50,8 Mb
Release : 2010-05-21
Category : Computers
ISBN : 9783642132773
This book and its sister volume constitutes the proceedings of the 7th International Symposium on Neural Networks, ISNN 2010, held in Shanghai, China, June 6-9, 2010. The 170 revised full papers of Part I and Part II were carefully selected from 591 submissions and focus on topics such as Neurophysiological Foundation, Theory and Models, Learning and Inference, and Neurodynamics. The second volume, Part II (LNCS 6064) covers the following 5 topics: SVM and Kernel Methods, Vision and Image, Data Mining and Text Analysis, BCI and Brain Imaging, and applications.
Author : Cornelis Roos,Tamás Terlaky,J.-Ph. Vial
Publisher : Springer Science & Business Media
Page : 501 pages
File Size : 54,6 Mb
Release : 2006-02-08
Category : Mathematics
ISBN : 9780387263793
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.
Author : Levent Tuncel
Publisher : Unknown
Page : 32 pages
File Size : 53,7 Mb
Release : 1992
Category : Electronic
ISBN : CORNELL:31924063436335
Author : Tamás Terlaky
Publisher : Springer Science & Business Media
Page : 544 pages
File Size : 41,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461334491
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).
Author : Anonim
Publisher : Unknown
Page : 994 pages
File Size : 41,9 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015082440887
Author : Rangarajan Bharath Kumar
Publisher : Unknown
Page : 260 pages
File Size : 51,7 Mb
Release : 2004
Category : Electronic
ISBN : CORNELL:31924100459019
Author : L.T. Watson,M. Bartholomew-Biggs,J.A. Ford
Publisher : Gulf Professional Publishing
Page : 392 pages
File Size : 53,8 Mb
Release : 2001-03-28
Category : Mathematics
ISBN : 0444505997
After a review of historical developments in convergence analysis for Newton's and Newton-like methods, 18 papers deal in depth with various classical, or neo-classical approaches, as well as newer ideas on optimization and solving linear equations. A sampling of topics: truncated Newton methods, sequential quadratic programming for large- scale nonlinear optimization, and automatic differentiation of algorithms. This monograph, one of seven volumes in the set, is also published as the Journal of Computational and Applied Mathematics; v.124 (2000). Indexed only by author. c. Book News Inc.
Author : Yurii Nesterov,Arkadii Nemirovskii
Publisher : SIAM
Page : 414 pages
File Size : 49,5 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 1611970792
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.
Author : Anonim
Publisher : Unknown
Page : 2304 pages
File Size : 47,8 Mb
Release : 1997
Category : Electrical engineering
ISBN : OSU:32435059589309
Author : Yinyu Ye
Publisher : John Wiley & Sons
Page : 440 pages
File Size : 45,6 Mb
Release : 2011-10-11
Category : Mathematics
ISBN : 9781118030950
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.