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.
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.
Produktdetails
Produktdetails
Lecture Notes in Economics and Mathematical Systems 298
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.
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.
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