Generalized convexity and concavity of the optimal value function in nonlinear programming |
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Authors: | Jerzy Kyparisis Anthony V. Fiacco |
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Affiliation: | (1) Department of Decision Sciences, Florida International University, 33199 Miami, FL, USA;(2) Department of Operations Research, The George Washington Univesity, DC 20052 Washington, USA |
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Abstract: | In this paper we consider generalized convexity and concavity properties of the optimal value functionf * for the general parametric optimization problemP(ε) of the form min x f(x, ε) s.t.x∈R(ε). Many results on convexity and concavity characterizations off * were presented by the authors in a previous paper. Such properties off * and the solution set mapS * form an important part of the theoretical basis for sensitivity, stability and parametric analysis in mathematical optimization. We give sufficient conditions for several types of generalized convexity and concavity off *, in terms of respective generalized convexity and concavity assumptions onf and convexity and concavity assumptions on the feasible region point-to-set mapR. Specializations of these results to the parametric inequality-equality constrained nonlinear programming problem are provided. Research supported by Grant ECS-8619859, National Science Foundation and Contract N00014-86-K-0052, Office of Naval Research. |
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Keywords: | Nonlinear programming parametric analysis generalized convexity optimal value function point-to-set mappings |
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