Convex Parametric Programming in Abstract Spaces
This article studies stability and optimality for convex parametric programming models in abstract spaces. Necessary conditions for continuity of the feasible set mapping are given in complete metric spaces. This continuity is characterized for models in which the space of decision variables is refl...
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| Vydané v: | Optimization Ročník 51; číslo 6; s. 841 - 861 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Taylor & Francis Group
01.12.2002
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| Predmet: | |
| ISSN: | 0233-1934, 1029-4945 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | This article studies stability and optimality for convex parametric programming models in abstract spaces. Necessary conditions for continuity of the feasible set mapping are given in complete metric spaces. This continuity is characterized for models in which the space of decision variables is reflexive Banach space. The main result on optimality characterizes locally optimal parameters relative to stable perturbations of the parameter. The result is stated in terms of the existence of a saddle-point for a Lagrangian that uses a finite Borel measure. It does not hold for unstable perturbations even if the model is finite dimensional. The results are applicable to various formulations of control and optimal control problems. |
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| ISSN: | 0233-1934 1029-4945 |
| DOI: | 10.1080/0233193021000015659 |