Gintautas Dzemyda, Vydunas ?altenis, Antanas Zilinskas

Stochastic and Global Optimization

March 2002, ISBN 1-4020-0484-2, Hardbound

Book Series: NONCONVEX OPTIMIZATION AND ITS APPLICATIONS : Volume 59

This book is dedicated to the 70th birthday of Professor J. Mockus, whose scientific interests include theory and applications of global and discrete optimization, and stochastic programming. The papers for the book were selected because they relate to these topics and also satisfy the criterion of theoretical soundness combined with practical applicability. In addition, the methods for statistical analysis of extremal problems are covered. Although statistical approach to global and discrete optimization is emphasized, applications to optimal design and to mathematical finance are also presented. The results of some subjects (e.g., statistical models based on one-dimensional global optimization) are summarized and the prospects for new developments are justified.

Audience: Practitioners, graduate students in mathematics, statistics, computer science and engineering.

Contents and Contributors

The Jubilee of Prof. dr. Habil. Jonas Mockus. 1. Topographical Differential Evolution Using Pre-calculated Differentials; M.M. Ali, A. Torn. 2. Optimal Tax Depreciation in Stochastic Investment Model; V.I. Arkin, A.D. Slastnikov. 3. Global Optimisation of Chemical Process Flowsheets; I.D.L. Bogle, R.P. Byrne. 4. One-dimensional Global Optimization Based on Statistical Models; J.M. Calvin, A. Zilinskas. 5. Animated Visual Analysis of Extremal Problems; G. Dzemyda. 6. Test Problems for Lipschitz Univariate Global Optimization with Multiextremal Constraints; D. Famularo, P. Pugliese, Y.D. Sergeyev. 7. Numerical Techniques in Applied Multistage Stochastic Programming; K. Frauendorfer, G. Haarbrucker. 8. On the Efficiency and Effectiveness of Controlled Random Search; E.M.T. Hendrix, P.M. Ortigosa, I. Garcia. 9. Discrete Backtracking Adaptive Search for Global Optimization; B.P. Kristinsdottir, Z.B. Zabinsky, G.R. Wood. 10. Parallel Branch-and-bound Attraction Based Methods for Global Optimization; K. Madsen, J. Zilinskas. 11. On Solution of Stochastic Linear Programs by Discretization Methods; K. Marti. 12. The Structure of Multivariate Models and the Range of Definition; V. ?altenis, V. Tie?is. 13. Optimality Criteria for Investment Projects Under Uncertainty; S.A. Smolyak.

Diethard Klatte, Bernd Kummer

Nonsmooth Equations in Optimization
Regularity, Calculus, Methods and Applications

May 2002, ISBN 1-4020-0550-4, Hardbound

The book establishes links between regularity and derivative concepts of nonsmooth analysis and studies of solution methods and stability for optimization, complementarity and equilibrium problems. In developing necessary tools, it presents, in particular:

・an extended analysis of Lipschitz functions and the calculus of their generalized derivatives, including regularity, ・successive approximation and implicit functions for multivalued mappings;
・a unified theory of Lipschitzian critical points in optimization and other variational problems, with relations to 　　reformulations by penalty, barrier and NCP functions;
・an analysis of generalized Newton methods based on linear and nonlinear approximations;
・the interpretation of hypotheses, generalized derivatives and solution methods in terms of original data and quadratic 　　approximations;
・a rich collection of instructive examples and exercises.
・Audience: Researchers, graduate students and practitioners in various fields of applied mathematics, engineering, OR and 　　economics. Also university teachers and advanced students who wish to get insights into problems, future directions and 　　recent developments.

Contents

Introduction. List of Results. Basic Notation. 1. Basic Concepts. 2. Regularity and Consequences. 3. Characterizations of Regularity by Derivatives. 4. Nonlinear Variations and Implicit Functions. 5. Closed Mappings in Finite Dimension. 6. Analysis of Generalized Derivatives. 7. Critical Points and Generalized Kojima-Functions. 8. Parametric Optimization Problems. 9. Derivatives and Regularity of Further Nonsmooth Maps. 10. Newton's Method for Lipschitz Equations. 11. Particular Newton Realizations and Solution Methods. 12. Basic Examples and Exercises. Appendix. Bibliography. Index.

Ferenc Weisz

Summability of Multi-Dimensional Fourier Series
and Hardy Spaces

May 2002, ISBN 1-4020-0564-4, Hardbound

Book Series: MATHEMATICS AND ITS APPLICATIONS : Volume 541

This is the first monograph which considers the theory of more-parameter dyadic and classical Hardy spaces. In this book a new application of martingale and distribution theories is dealt with. The theories of the multi-parameter dyadic martingale and the classical Hardy spaces are applied in Fourier analysis. Several summability methods of d-dimensional trigonometric-, Walsh-, spline-, and Ciesielski-Fourier series and Fourier transforms as well as the d-dimensional dyadic derivative are investigated. The boundedness of the maximal operators of the summations on Hardy spaces, weak (L1, L1) inequalities and a.e. convergence results for the d-dimensional Fourier series are proved.

Audience: This book will be useful for researchers as well as for graduate or postgraduate students whose work involves Fourier analysis, approximations and expansions, sequences, series, summability, probability theory, stochastic processes, several complex variables, and analytic spaces.

Contents

Preface. Acknowledgments. 1. Multi-Dimensional Dyadic Hardy Spaces. 2. Multi-Dimensional Classical Hardy Spaces. 3. Summability of D-Dimensional Walsh-Fourier Series. 4. The D-Dimensional Dyadic Derivative. 5. Summability of D-Dimensional Trigonometric-Fourier Series. 6. Summability of D-Dimensional Fourier Transforms. 7. Spline and Ciesielski Systems. References. Index

A.G. Chentsov, Svetlana I. Morina

Extensions and Relaxations

May 2002, ISBN 1-4020-0579-2, Hardbound

Book Series: MATHEMATICS AND ITS APPLICATIONS : Volume 542

In this book a general topological construction of extension is proposed for problems of attainability in topological spaces under perturbation of a system of constraints. This construction is realized in a special class of generalized elements defined as finitely additive measures. A version of the method of programmed iterations is constructed. This version realizes multi-valued control quasistrategies, which guarantees the solution of the control problem that consists in guidance to a given set under observation of phase constraints.

Audience: The book will be of interest to researchers, and graduate students in the field of optimal control, mathematical systems theory, measure and integration, functional analysis, and general topology.

Contents

Preface. 1. Phase Constraints and Boundary Conditions in Linear Control Problems. 2. General Structures. 3. Topological Constructions of Extensions and Relaxations. 4. Elements of Measure Theory and Extension Constructions. 5. Compactifications and Problems of Integration. 6. Non-Anticipating Procedures of Control and Iteration Methods for Constructing Them. 7. An Extension Construction for Set-Valued Quasi-Strategies. Conclusion. References. Notation. Index.