Interior Point Techniques in Optimization

Complementarity, Sensitivity and Algorithms

Author: B. Jansen

Publisher: Springer Science & Business Media

ISBN: 1475755619

Category: Mathematics

Page: 280

View: 3017

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.
Posted in Mathematics

Complementarity: Applications, Algorithms and Extensions

Author: Michael C. Ferris,Olvi L. Mangasarian,Jong-Shi Pang

Publisher: Springer Science & Business Media

ISBN: 1475732791

Category: Computers

Page: 404

View: 1787

This volume presents state-of-the-art complementarity applications, algorithms, extensions and theory in the form of eighteen papers. These at the International Conference on Com invited papers were presented plementarity 99 (ICCP99) held in Madison, Wisconsin during June 9-12, 1999 with support from the National Science Foundation under Grant DMS-9970102. Complementarity is becoming more widely used in a variety of appli cation areas. In this volume, there are papers studying the impact of complementarity in such diverse fields as deregulation of electricity mar kets, engineering mechanics, optimal control and asset pricing. Further more, application of complementarity and optimization ideas to related problems in the burgeoning fields of machine learning and data mining are also covered in a series of three articles. In order to effectively process the complementarity problems that arise in such applications, various algorithmic, theoretical and computational extensions are covered in this volume. Nonsmooth analysis has an im portant role to play in this area as can be seen from articles using these tools to develop Newton and path following methods for constrained nonlinear systems and complementarity problems. Convergence issues are covered in the context of active set methods, global algorithms for pseudomonotone variational inequalities, successive convex relaxation and proximal point algorithms. Theoretical contributions to the connectedness of solution sets and constraint qualifications in the growing area of mathematical programs with equilibrium constraints are also presented. A relaxation approach is given for solving such problems. Finally, computational issues related to preprocessing mixed complementarity problems are addressed.
Posted in Computers

Large-scale Optimization

Problems and Methods

Author: Vladimir Tsurkov

Publisher: Springer Science & Business Media

ISBN: 1475732430

Category: Computers

Page: 312

View: 5500

Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem. Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are categorized. The issues of loss of accuracy, recovery of original variables (disaggregation), and compatibility conditions are analyzed in detail. The method of iterative aggregation in large-scale problems is studied. For fixed weights, successively simpler aggregated problems are solved and the convergence of their solution to that of the original problem is analyzed. An introduction to block integer programming is considered. Duality theory, which is widely used in continuous block programming, does not work for the integer problem. A survey of alternative methods is presented and special attention is given to combined methods of decomposition. Block problems in which the coupling variables do not enter the binding constraints are studied. These models are worthwhile because they permit a decomposition with respect to primal and dual variables by two-level algorithms instead of three-level algorithms. Audience: This book is addressed to specialists in operations research, optimization, and optimal control.
Posted in Computers

Interior Point Methods of Mathematical Programming

Author: Tamas Terlaky

Publisher: Springer Science & Business Media

ISBN: 9780792342014

Category: Mathematics

Page: 530

View: 9827

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).
Posted in Mathematics

Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 8363

Posted in American literature

INFOR.

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Electronic data processing

Page: N.A

View: 4814

Posted in Electronic data processing

Forthcoming Books

Author: Rose Arny

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 5207

Posted in American literature

Handbook of global optimization

Author: Reiner Horst,Panos M. Pardalos

Publisher: Kluwer Academic Pub

ISBN: 9780792331209

Category: Business & Economics

Page: 880

View: 5608

Global optimization is concerned with the computation and characterization of global optima of nonlinear functions. During the past three decades the field of global optimization has been growing at a rapid pace, and the number of publications on all aspects of global optimization has been increasing steadily. Many applications, as well as new theoretical, algorithmic, and computational contributions have resulted. The Handbook of Global Optimization is the first comprehensive book to cover recent developments in global optimization. Each contribution in the Handbook is essentially expository in nature, but scholarly in its treatment. The chapters cover optimality conditions, complexity results, concave minimization, DC programming, general quadratic programming, nonlinear complementarity, minimax problems, multiplicative programming, Lipschitz optimization, fractional programming, network problems, trajectory methods, homotopy methods, interval methods, and stochastic approaches. The Handbook of Global Optimization is addressed to researchers in mathematical programming, as well as all scientists who use optimization methods to model and solve problems.
Posted in Business & Economics

Conference Papers

Author: N.A

Publisher: N.A

ISBN: 9780780354791

Category: Electric power

Page: 353

View: 7693

Posted in Electric power

Conference Proceedings

Author: N.A

Publisher: N.A

ISBN: 9780780354791

Category: Computers

Page: 353

View: 4805

Posted in Computers

Linear Programming

Foundations and Extensions

Author: Robert J Vanderbei

Publisher: Springer Science & Business Media

ISBN: 1475756623

Category: Business & Economics

Page: 450

View: 3589

This book provides an introduction to optimization. It details constrained optimization, beginning with a substantial treatment of linear programming and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Coverage underscores the purpose of optimization: to solve practical problems on a computer. C programs that implement the major algorithms and JAVA tools are available online.
Posted in Business & Economics

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 8706

Posted in Mathematics

Linear and Integer Programming

Theory and Practice, Second Edition

Author: Gerard Sierksma

Publisher: CRC Press

ISBN: 9780824706739

Category: Mathematics

Page: 656

View: 4930

"Combines the theoretical and practical aspects of linear and integer programming. Provides practical case studies and techniques, including rounding-off, column-generation, game theory, multiobjective optimization, and goal programming, as well as real-world solutions to the transportation and transshipment problem, project scheduling, and decentralization."
Posted in Mathematics

Simulationsmethoden

Author: Hans-Ulrich Zschiesche

Publisher: Springer-Verlag

ISBN: 3322964248

Category: Technology & Engineering

Page: 60

View: 8637

Im allgemeinsten Sinne versteht man unter Simulation die Untersuchung eines Prozesses oder eines Systems mit Hilfe eines Ersatzsystems. Häufig zitierte Beispiele für derartige Simulationen sind Simulatoren bei der Ausbildung von Flugzeugpiloten oder in Fahrschulen. Die Gründe für ein derartiges Vorgehen liegen auf der Hand. Es sind in erster Linie geringere Kosten und geringere Gefahr; in vielen prakiischen Fällen sind darüber hinaus Untersuchungen am realen System gar nicht möglich, wie spätere Beispiele zeigen werden. Wichtige Ersatzsysteme für Simulationen stellen die mathematischen Modelle dar, die den zu untersuchenden Prozeß beschreiben und die auf einem Digitalrechner aus gewertet werden. In einem solchen Falle spricht man von digitaler Simulation oder Simulation im engeren Sinne. Im folgenden werden wir uns mi~ derartigen Simula tionen beschäftigen. Meist tritt noch ein weiteres Moment hinzu, nämlich das Experimentieren mit einem solchen Modell. Das ist darin begründet, daß die Modelle oft sehr kompliziert und umfangreich sind, so daß keine expliziten mathematischen Methoden zur Be stimmung von Optimallösungen vorliegen; diese können dann nur über Varianten rechnungen ermittelt werden. Aus diesen Gründen spricht man im Zusammenhang mit der Simulation oft auch von experimenteller Mathematik.
Posted in Technology & Engineering