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.

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.

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.

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.

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."

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.

Download or read book Acta Numerica 1993 Volume 2 written by Arieh Iserles and published by Cambridge University Press. This book was released on 1993-04-30 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing the tradition established with the 1992 volume, this 1993's Acta Numerica presents six invited papers on a broad range of topics from numerical analysis. Papers treat each topic at a level intelligible by any numerical analyst from graduate student to professional.

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.

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.

Download or read book Primal dual Methods for Linear Programming written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and published by . This book was released on 1991 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Large Scale Scientific Computing written by Ivan Lirkov and published by Springer. This book was released on 2010-05-10 with total page 855 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Large-Scale Scientific Computations, LSSC 2009, held in Sozopol, Bulgaria, in June 2009. The 93 revised full papers presented together with 5 plenary and invited papers were carefully reviewed and selected from numerous submissions for inclusion in the book. The papers are organized in topical sections on multilevel and multiscale preconditioning methods multilevel and multiscale methods for industrial applications, environmental modeling, control and uncertain systems, application of metaheuristics to large scale problems, monte carlo: methods, applications, distributed computing, grid and scientific and engineering applications, reliable numerical methods for differential equations, novel applications of optimization ideas to the numerical Solution of PDEs, and contributed talks.

Download or read book Nonlinear Equations and Optimisation written by L.T. Watson and published by Gulf Professional Publishing. This book was released on 2001-03-28 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Download or read book Recent Trends in Optimization Theory and Applications written by Ratan Prakash Agarwal and published by World Scientific. This book was released on 1995 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: World Scientific Series in Applicable Analysis (WSSIAA) aims at reporting new developments of high mathematical standard and current interest. Each volume in the series shall be devoted to the mathematical analysis that has been applied or potentially applicable to the solutions of scientific, engineering, and social problems. This volume contains 30 research articles on the theory of optimization and its applications by the leading scientists in the field. It is hoped that the material in the present volume will open new vistas in research.Contributors: B D O Anderson, M Bertaja, O J Boxma, O Burdakov, A Cantoni, D J Clements, B D Craven, J B Cruz, Jr., P Diamond, S V Drakunov, Y G Evtushenko, N M Filatov, I Galligani, J C Geromel, F Giannessi, M J Grimble, G O Guardabassi, D-W Gu, C H Houpis, D G Hull, C Itiki, X Jian, M A Johnson, R E Kalaba, J C Kalkkuhl, M R Katebi, T J Kim, P Kloeden, T Kobylarz, A J Laub, C S Lee, G Leitmann, B-G Liu, J Liu, Z-Q Luo, K A Lurie, P Maponi, J B Matson, A Mess, G Pacelli, M Pachter, I Postlethwaite, T Rapcsak, M C Recchioni, Y Sakawa, S V Savastyuk, K Schittkowski, Y Shi, M A Sikora, D D Siljak, K L Teo, C Tovey, P Tseng, F E Udwadia, H Unbehauen, A Vladimirov, B Vo, J F Whidborne, R Xu, P L Yu, V G Zhadan, F Zirilli.

Download or read book An Introduction to Linear Programming and Game Theory written by Paul R. Thie and published by John Wiley & Sons. This book was released on 2011-09-15 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Second Edition: "This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications." —Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems. This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications. Additional features of the Third Edition include: A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models Revised proofs and a discussion on the relevance and solution of the dual problem A section on developing an example in Data Envelopment Analysis An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science.

Download or read book The Linear Complementarity Problem written by Richard W. Cottle and published by SIAM. This book was released on 2009-08-27 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: A revised edition of the standard reference on the linear complementarity problem.

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.