• Business & Economics

Topics in Nonconvex Optimization

Theory and Applications
Author: Shashi K. Mishra
Publisher: Springer Science & Business Media
ISBN: 9781441996404
Category: Business & Economics
Page: 270
View: 4288
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.

    • Mathematics

Recent Advances in Nonsmooth Optimization


Author: Dingzhu Du,Liqun Qi,Robert S. Womersley
Publisher: World Scientific
ISBN: 9789810222659
Category: Mathematics
Page: 472
View: 3512
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.

    • Business & Economics

Nonlinear Analysis and Variational Problems

In Honor of George Isac
Author: Panos M. Pardalos,Themistocles Rassias,Akhtar A. Khan
Publisher: Springer Science & Business Media
ISBN: 1441901582
Category: Business & Economics
Page: 490
View: 4903
The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.

    • Mathematics

Complementarity, Equilibrium, Efficiency and Economics


Author: G. Isac,V.A. Bulavsky,Vyacheslav V. Kalashnikov
Publisher: Springer Science & Business Media
ISBN: 1475736231
Category: Mathematics
Page: 449
View: 4342
In complementarity theory, which is a relatively new domain of applied mathematics, several kinds of mathematical models and problems related to the study of equilibrium are considered from the point of view of physics as well as economics. In this book the authors have combined complementarity theory, equilibrium of economical systems, and efficiency in Pareto's sense. The authors discuss the use of complementarity theory in the study of equilibrium of economic systems and present results they have obtained. In addition the authors present several new results in complementarity theory and several numerical methods for solving complementarity problems associated with the study of economic equilibrium. The most important notions of Pareto efficiency are also presented. Audience: Researchers and graduate students interested in complementarity theory, in economics, in optimization, and in applied mathematics.

    • Business & Economics

Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization


Author: Qamrul Hasan Ansari,C. S. Lalitha,Monika Mehta
Publisher: CRC Press
ISBN: 1439868204
Category: Business & Economics
Page: 280
View: 4642
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.

    • Mathematics

Complementarity Problems


Author: George Isac
Publisher: Berlin : Springer-Verlag
ISBN: 9780387562513
Category: Mathematics
Page: 297
View: 6600
The study of complementarity problems is now an interesting mathematical subject with many applications in optimization, game theory, stochastic optimal control, engineering, economics etc. This subject has deep relations with important domains of fundamental mathematics such as fixed point theory, ordered spaces, nonlinear analysis, topological degree, the study of variational inequalities and also with mathematical modeling and numerical analysis. Researchers and graduate students interested in mathematical modeling or nonlinear analysis will find here interesting and fascinating results.






    • Science

Leray–Schauder Type Alternatives, Complementarity Problems and Variational Inequalities


Author: George Isac
Publisher: Springer Science & Business Media
ISBN: 0387329005
Category: Science
Page: 352
View: 9111
Complementarity theory, a relatively new domain in applied mathematics, has deep connections with several aspects of fundamental mathematics and also has many applications in optimization, economics and engineering. The study of variational inequalities is another domain of applied mathematics with many applications to the study of certain problems with unilateral conditions. This book is the first to discuss complementarity theory and variational inequalities using Leray Schauder type alternatives. The ideas and method presented in this book may be considered as a starting point for new developments.

    • American literature

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: 4743

    • Probabilities

Lecture Notes in Mathematics


Author: Dominique Bakry,R. D. Gill,Stanislav A. Molchanov,Pierre Bernard
Publisher: Springer
ISBN: 9783540582083
Category: Probabilities
Page: 419
View: 1994
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.

    • Mathematics

Difference Equations and Inequalities

Theory, Methods, and Applications
Author: Ravi P. Agarwal
Publisher: CRC Press
ISBN: 9781420027020
Category: Mathematics
Page: 1000
View: 9384
A study of difference equations and inequalities. This second edition offers real-world examples and uses of difference equations in probability theory, queuing and statistical problems, stochastic time series, combinatorial analysis, number theory, geometry, electrical networks, quanta in radiation, genetics, economics, psychology, sociology, and other disciplines. It features 200 new problems, 400 additional references, and a new chapter on the qualitative properties of solutions of neutral difference equations.


    • Mathematics

Statistical mechanics and fractals


Author: R. L. Dobrushin,Shigeo Kusuoka
Publisher: Springer Verlag
ISBN: N.A
Category: Mathematics
Page: 98
View: 1051
The Nankai Institute of Mathematics held a special Year in Probability and Statistics during the academic year of 1988-1989. We had over 150 specialists, professors and graduate students, who participated in this Special Year from August 1988 to May 1989. More than twenty outstanding probabilists and statisticians from several countries were invited to give lectures and talks. This volume contains two lectures, one is written by Professor R. L. Dobrushin, and the other one by Professor S. Kusuoka.

    • Mathematics

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
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: 440
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.

    • Mathematics

Convexity and Optimization in Banach Spaces


Author: Viorel Barbu,Teodor Precupanu
Publisher: Springer Science & Business Media
ISBN: 940072246X
Category: Mathematics
Page: 368
View: 885
An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application. This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems. Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.

    • Mathematics

Seminaire de Probabilites XXXIII


Author: J. Azema,M. Emery,M. Ledoux,M. Yor
Publisher: Springer
ISBN: N.A
Category: Mathematics
Page: 419
View: 4660
Besides topics traditionally found in the Séminaire de Probabilités (Martingale Theory, Stochastic Processes, questions of general interest in Probability Theory), this volume XXXIII presents nine contributions to the study of filtrations up to isomorphism. It also contains three graduate courses: Dynamics of stochastic algorithms, by M. Benaim; Simulated annealing algorithms and Markov chains with rare transitions, by O. Catoni; and Concentration of measure and logarithmic Sobolev inequalities, by M. Ledoux. These up to date courses present the state of the art in three matters of interest to students in theoretical or applied Probability Theory, and to researchers as well.