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.
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ISBN-13
978-3-642-46623-6 (9783642466236)
DOI
10.1007/978-3-642-46623-6
Schweitzer Klassifikation
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.
