Das lineare Komplementaritätsproblem

Eine Einführung

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Author: Uwe Schäfer

Publisher: Springer-Verlag

ISBN: 3540797351

Category: Mathematics

Page: 268

View: 7131

Wer Querverbindungen in der Mathematik mag, den interessiert mit Sicherheit auch das lineare Komplementaritätsproblem. Denn viele mathematische Problemstellungen, die auf den ersten Blick nichts miteinander zu tun haben, lassen sich in ein lineares Komplementaritätsproblem überführen. Das Buch stellt erstmals auf Deutsch viele dieser Problemstellungen vor. Zur Lösung werden sowohl direkte als auch iterative Verfahren betrachtet. Die Lösungen zu den in den Kapiteln gestellten Aufgaben sind ausgearbeitet, detaillierte Abbildungen runden das Buch ab.

Recent Advances in Nonsmooth Optimization

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Author: Dingzhu Du,Liqun Qi,Robert S. Womersley

Publisher: World Scientific

ISBN: 9789810222659

Category: Mathematics

Page: 472

View: 9725

Nonsmooth optimization covers the minimization or maximization of functions which do not have the differentiability properties required by classical methods. The field of nonsmooth optimization is significant, not only because of the existence of nondifferentiable functions arising directly in applications, but also because several important methods for solving difficult smooth problems lead directly to the need to solve nonsmooth problems, which are either smaller in dimension or simpler in structure.This book contains twenty five papers written by forty six authors from twenty countries in five continents. It includes papers on theory, algorithms and applications for problems with first-order nondifferentiability (the usual sense of nonsmooth optimization) second-order nondifferentiability, nonsmooth equations, nonsmooth variational inequalities and other problems related to nonsmooth optimization.

Complementarity and Variational Inequalities in Electronics

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Author: Daniel Goeleven

Publisher: Academic Press

ISBN: 0128133902

Category: Mathematics

Page: 208

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Complementarity and Variational Inequalities in Electronics evaluates the main mathematical models relevant to the study of electrical network problems involving devices. The book focuses on complementarity problems, variational inequalities and non-regular dynamical systems which are well-known for their applications in mechanics and economics, but rarely target electrical applications. The book uses these tools to review the qualitative properties of devices, including slicers, amplitude selectors, sampling gates, operational amplifiers, and four-diode bridge full-wave rectifiers. Users will find demonstrations on how to compute optimized output signal relevant to potentially superior applications. In addition, the book describes how to determine the stationary points of dynamical circuits and to determine the corresponding Lyapunov stability and attractivity properties, topics of major importance for further dynamical analysis and control. Hemivariational inequalities are also covered in some depth relevant to application in thyristor devices. Reviews the main mathematical models applicable to the study of electrical networks involving diodes and transistors Focuses on theoretical existence and uniqueness of a solution, stability of stationary solutions, and invariance properties Provides realistic complementarity and variational problems to illustrate theoretical results Evaluates applications of the theory across many devices, including slicers, amplitude selectors, sampling gates, operational amplifiers, and four-diode bridge full-wave rectifiers Details both fully developed mathematical proofs and common models used in electronics Provides a comprehensive literature review, including thousands of relevant references

Topics in Nonconvex Optimization

Theory and Applications

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Author: Shashi K. Mishra

Publisher: Springer Science & Business Media

ISBN: 9781441996404

Category: Business & Economics

Page: 270

View: 4047

Nonconvex Optimization is a multi-disciplinary research field that deals with the characterization and computation of local/global minima/maxima of nonlinear, nonconvex, nonsmooth, discrete and continuous functions. Nonconvex optimization problems are frequently encountered in modeling real world systems for a very broad range of applications including engineering, mathematical economics, management science, financial engineering, and social science. This contributed volume consists of selected contributions from the Advanced Training Programme on Nonconvex Optimization and Its Applications held at Banaras Hindu University in March 2009. It aims to bring together new concepts, theoretical developments, and applications from these researchers. Both theoretical and applied articles are contained in this volume which adds to the state of the art research in this field. Topics in Nonconvex Optimization is suitable for advanced graduate students and researchers in this area.

Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization

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Author: Qamrul Hasan Ansari,C. S. Lalitha,Monika Mehta

Publisher: CRC Press

ISBN: 1439868204

Category: Business & Economics

Page: 280

View: 4240

Until now, no book addressed convexity, monotonicity, and variational inequalities together. Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization covers all three topics, including new variational inequality problems defined by a bifunction. The first part of the book focuses on generalized convexity and generalized monotonicity. The authors investigate convexity and generalized convexity for both the differentiable and nondifferentiable case. For the nondifferentiable case, they introduce the concepts in terms of a bifunction and the Clarke subdifferential. The second part offers insight into variational inequalities and optimization problems in smooth as well as nonsmooth settings. The book discusses existence and uniqueness criteria for a variational inequality, the gap function associated with it, and numerical methods to solve it. It also examines characterizations of a solution set of an optimization problem and explores variational inequalities defined by a bifunction and set-valued version given in terms of the Clarke subdifferential. Integrating results on convexity, monotonicity, and variational inequalities into one unified source, this book deepens your understanding of various classes of problems, such as systems of nonlinear equations, optimization problems, complementarity problems, and fixed-point problems. The book shows how variational inequality theory not only serves as a tool for formulating a variety of equilibrium problems, but also provides algorithms for computational purposes.

Leray–Schauder Type Alternatives, Complementarity Problems and Variational Inequalities

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Author: George Isac

Publisher: Springer Science & Business Media

ISBN: 0387329005

Category: Mathematics

Page: 338

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This book is the first to discuss complementarity theory and variational inequalities using Leray–Schauder type alternatives. Complementarity theory, a relatively new domain in applied mathematics, has deep connections with several aspects of fundamental mathematics. The ideas and method presented in this book may be considered as a starting point for new developments. The book presents a new kind of application for the Leray–Schauder principle.

Lecture Notes in Mathematics

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Author: Dominique Bakry,R. D. Gill,Stanislav A. Molchanov,Pierre Bernard

Publisher: Springer

ISBN: 9783540582083

Category: Probabilities

Page: 419

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This book contains work-outs of the notes of three 15-hour courses of lectures which constitute surveys on the concerned topics given at the St. Flour Probability Summer School in July 1992. The first course, by D. Bakry, is concerned with hypercontractivity properties and their use in semi-group theory, namely Sobolev and Log Sobolev inequa- lities, with estimations on the density of the semi-groups. The second one, by R.D. Gill, is about statistics on survi- val analysis; it includes product-integral theory, Kaplan- Meier estimators, and a look at cryptography and generation of randomness. The third one, by S.A. Molchanov, covers three aspects of random media: homogenization theory, loca- lization properties and intermittency. Each of these chap- ters provides an introduction to and survey of its subject.

State of the art in global optimization

computational methods and applications

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Author: Christodoulos A. Floudas,Panos M. Pardalos

Publisher: Kluwer Academic Pub

ISBN: 9780792338383

Category: Mathematics

Page: 651

View: 6586

Optimization problems abound in most fields of science, engineering, and technology. In many of these problems it is necessary to compute the global optimum (or a good approximation) of a multivariable function. The variables that define the function to be optimized can be continuous and/or discrete and, in addition, many times satisfy certain constraints. Global optimization problems belong to the complexity class of NP-hard problems. Such problems are very difficult to solve. Traditional descent optimization algorithms based on local information are not adequate for solving these problems. In most cases of practical interest the number of local optima increases, on the average, exponentially with the size of the problem (number of variables). Furthermore, most of the traditional approaches fail to escape from a local optimum in order to continue the search for the global solution. Global optimization has received a lot of attention in the past ten years, due to the success of new algorithms for solving large classes of problems from diverse areas such as computational chemistry and biology, structural optimization, computer sciences, operations research, economics, and engineering design and control. This book contains refereed invited papers presented at the conference on 'State of the Art in Global Optimization: Computational Methods and Applications' held at Princeton University, April 28-30, 1995. The conference presented current research on global optimization and related applications in science and engineering. The papers included in this book cover a wide spectrum of approaches for solving global optimization problems and applications. The book will be a valuable source of information to faculty, students and researchers in optimization, engineering, mathematics, computer sciences, and related areas.

Vector Bundles on Curves - New Directions

Lectures Given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), Held in Cetraro (Cosenza), Italy, June 19-27, 1995

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Author: Shrawan Kumar,Gérard Laumon,Ulrich Stuhler,M.S. Narasimhan,Centro internazionale matematico estivo. Session,Centro internazionale matematico estivo,Lecture Notes in Mathematics Staff

Publisher: Springer Verlag

ISBN: N.A

Category: Mathematics

Page: 193

View: 642

The book gives a survey of some recent developments in the theory of bundles on curves arising out of the work of Drinfeld and from insights coming from Theoretical Physics. It deals with: 1. The relation between conformal blocks and generalised theta functions (Lectures by S. Kumar) 2. Drinfeld Shtukas (Lectures by G. Laumon) 3. Drinfeld modules and Elliptic Sheaves (Lectures by U. Stuhler) The latter topics are useful in connection with Langlands programme for function fields. The contents of the book would give a comprehensive introduction of these topics to graduate students and researchers.

Books in Print

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

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Topological methods for variational problems with symmetries

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Author: Thomas Bartsch

Publisher: Springer

ISBN: 9783540573784

Category: Mathematics

Page: 152

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The 18th International Workshop on Graph-Theoretic Concepts in Computer Science (WG '92) was held in Wiesbaden-Naurod, Germany, June 18-20, 1992. Itwas organized by the Department of Computer Science, Johann Wolfgang Goethe University, Frankfurt am Main. Contributions with original results inthe study and application of graph-theoretic concepts in various fields of computer science were solicited, and 72 papers were submitted and reviewed, from which 29 were selected for presentation at the workshop. The workshop was attended by 61 scientists from 16 countries. All 29 papers in the volume have undergone careful revision after the meeting, based on the discussions and comments from the audience and the referees. The volume is divided into parts on restricted graph classes, scheduling and related problems, parallel anbd distributed algorithms, combinatorial graph problems, graph decomposition, graph grammars and geometry, and modelling by graphs.

D-modules, representation theory, and quantum groups

lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Venezia, Italy, June 12-20, 1992

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Author: Louis Boutet de Monvel,Giuseppe Zampieri,Andrea D'Agnolo

Publisher: N.A

ISBN: 9783540574989

Category: Mathematics

Page: 217

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CONTENTS: L. Boutet de Monvel: Indice de systemes differentiels.- C. De Concini, C. Procesi: Quantum groups.- P. Schapira, J.P. Schneiders: Index theorems for R-constructible sheaves and for D-modules.- N. Berline, M. Vergne: The equivariant Chern character and index of G-invariant operators.