M. Kocvara - Böcker

This book presents an in-depth study and a solution technique for an important class of optimization problems. This class is characterized by special constraints - parameter-dependent convex programs, variational inequalities, or complementarity problems. All these so-called equilibrium constraints are mostly treated in a convenient form of generalized equations. The book begins with a chapter on auxiliary results followed by a description of the main numerical tools - a bundle method of nonsmooth optimization and a nonsmooth variant of Newton's method. Following this, stability and sensitivity theory for generalized equations is presented, based on the concept of strong regularity. This enables one to apply the generalized differential calculus for Lipschitz maps to derive optimality conditions and to arrive at a solution method. A large part of the book focuses on applications coming from continuum mechanics and mathematical economy. A series of nonacademic problems is introduced and analyzed in detail. Each problem is accompanied with examples that show the efficiency of the solution method.This book is addressed to applied mathematicians and engineers working in continuum mechanics, operations research and economic modelling. Students interested in optimization should also find the book useful.

This text contains results of research on: numerical solutions of Schrodinger-type problems; sampling theorems; numerical methods for large-scale non-convex quadratic programming; derivative-free algorithms; free material optimization; Moreau's sweeping process and a perspective on contemporary industrial mathematics work. The book also includes wavelet-based digital watermarking techniques and computer simulation of meteorological parameters. One chapter of the book is also devoted to the importance of strange attractors for industrial mathematics.

This book presents an in-depth study and a solution technique for an important class of optimization problems. This class is characterized by special constraints: parameter-dependent convex programs, variational inequalities or complementarity problems. All these so-called equilibrium constraints are mostly treated in a convenient form of generalized equations. The book begins with a chapter on auxiliary results followed by a description of the main numerical tools: a bundle method of nonsmooth optimization and a nonsmooth variant of Newton's method. Following this, stability and sensitivity theory for generalized equations is presented, based on the concept of strong regularity. This enables one to apply the generalized differential calculus for Lipschitz maps to derive optimality conditions and to arrive at a solution method. A large part of the book focuses on applications coming from continuum mechanics and mathematical economy. A series of nonacademic problems is introduced and analyzed in detail. Each problem is accompanied with examples that show the efficiency of the solution method.This book is addressed to applied mathematicians and engineers working in continuum mechanics, operations research and economic modelling. Students interested in optimization will also find the book useful.

An important objective of the study of mathematics is to analyze and visualize phenomena of nature and real world problems for its proper understanding. Gradually, it is also becoming the language of modem financial instruments. To project some of these developments, the conference was planned under the joint auspices of the Indian Society of Industrial and Applied mathematics (ISlAM) and Guru Nanak Dev University (G. N. D. U. ), Amritsar, India. Dr. Pammy Manchanda, chairperson of Mathematics Department, G. N. D. U. , was appointed the organizing secretary and an organizing committee was constituted. The Conference was scheduled in World Mathematics Year 2000 but, due one reason or the other, it could be held during 22. -25. January 2001. How­ ever, keeping in view the suggestion of the International Mathematics union, we organized two symposia, Role of Mathematics in industrial development and vice-versa and How image of Mathematics can be improved in public. These two symposia aroused great interest among the participants and almost everyone participated in the deliberations. The discussion in these two themes could be summarized in the lengthy following lines: "Tradition of working in isolation is a barrier for interaction with the workers in the other fields of science and engineering, what to talk of non-academic areas, specially the private sector of finance and industry. Therefore, it is essential to build bridges within in­ stitutions and between institutions.