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Robust Duality in Parametric Convex Optimization

Robust Duality in Parametric Convex Optimization Modelling of convex optimization in the face of data uncertainty often gives rise to families of parametric convex optimization problems. This motivates us to present, in this paper, a duality framework for a family of parametric convex optimization problems. By employing conjugate analysis, we present robust duality for the family of parametric problems by establishing strong duality between associated dual pair. We first show that robust duality holds whenever a constraint qualification holds. We then show that this constraint qualification is also necessary for robust duality in the sense that the constraint qualification holds if and only if robust duality holds for every linear perturbation of the objective function. As an application, we obtain a robust duality theorem for the best approximation problems with constraint data uncertainty under a strict feasibility condition. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Set-Valued and Variational Analysis Springer Journals

Robust Duality in Parametric Convex Optimization

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References (23)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Science+Business Media B.V.
Subject
Mathematics; Analysis; Geometry
ISSN
1877-0533
eISSN
1877-0541
DOI
10.1007/s11228-012-0219-y
Publisher site
See Article on Publisher Site

Abstract

Modelling of convex optimization in the face of data uncertainty often gives rise to families of parametric convex optimization problems. This motivates us to present, in this paper, a duality framework for a family of parametric convex optimization problems. By employing conjugate analysis, we present robust duality for the family of parametric problems by establishing strong duality between associated dual pair. We first show that robust duality holds whenever a constraint qualification holds. We then show that this constraint qualification is also necessary for robust duality in the sense that the constraint qualification holds if and only if robust duality holds for every linear perturbation of the objective function. As an application, we obtain a robust duality theorem for the best approximation problems with constraint data uncertainty under a strict feasibility condition.

Journal

Set-Valued and Variational Analysis – Springer Journals

Published: Jul 18, 2012

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