Integral Global Optimization: Theory, Implementation and Applications

by Soo H. Chew, Quan Zheng

Overview

This book treats the subject of global optimization with minimal restrictions on the behavior on the objective functions. In particular, optimal conditions were developed for a class of noncontinuous functions characterized by their having level sets that are robust. The integration-based approach contrasts with existing approaches which require some degree of convexity or differentiability of the objective function. Some computational results on a personal computer are presented.

Product Details

ISBN-13:	9783540187721
Publisher:	Springer Berlin Heidelberg
Publication date:	02/24/1988
Series:	Lecture Notes in Economics and Mathematical Systems , #298
Edition description:	Softcover reprint of the original 1st ed. 1988
Pages:	179
Product dimensions:	6.69(w) x 9.61(h) x 0.02(d)

Table of Contents

I Preliminary.- §1 Introduction.- §2 An Appropriate Concept of Measure.- II Integral Characterizations of Global Optimality.- §1 Mean Value Conditions.- §2 Variance and Higher Moment Conditions.- §3 The Constrained Cases.- §4 Penalty Global Optimality Conditions.- §5 Convex Programming.- §6 Optimality Conditions for Differentiable Functions.- §7 Integer and Mixed Programming.- §8 Optimality Conditions for a Class of Discontinuous Functions.- III Theoretical Algorithms and Techniques.- §1 The Mean Value-Level Set (M-L) Method.- §2 The Rejection and Reduction Methods.- §3 Global SUMT and Discontinuous Penalty Functions.- §4 The Nonsequential Penalty Method.- §5 The Technique of Adaptive Change of Search Domain.- §6 Stability of Global Minimization.- 6.1 Continuity of Mean Value.- 6.2 Stability of Global Minima.- §7 Lower Dimensional Approximation.- IV Monte Carlo Implementation.- §1 A Simple Model of Implemention.- §2 Statistical Analysis of the Simple Model.- §3 Strategies of Adaptive Change of Search Domains.- §4 Remarks on Other Models.- §5 Numerical Tests.- V Applications.- §1 Unconstrained Problems.- §2 Applications of the Rejection Method.- §3 Applications of the Reduction Method.- §4 An Application of the Penalty Method.- §5 An Application of Integer and Mixed Programming.