Integral Global Optimization de Soo H. Chew

Integral Global Optimization: Theory, Implementation and Applications: Lecture Notes in Economics and Mathematical Systems, cartea 298

Soo H. Chew

Quan Zheng

en Limba Engleză Paperback – 24 feb 1988

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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Specificații

ISBN-13: 9783540187721
ISBN-10: 3540187723
Pagini: 196
Ilustrații: VII, 179 p.
Dimensiuni: 170 x 244 x 10 mm
Greutate: 0.32 kg
Ediția:Softcover reprint of the original 1st ed. 1988
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes in Economics and Mathematical Systems

Locul publicării:Berlin, Heidelberg, Germany

Cuprins

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.