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Metric regularity in convex semi-infinite optimization under canonical perturbations


Canovas, M J; Klatte, D; Lopez, M A; Parra, J (2007). Metric regularity in convex semi-infinite optimization under canonical perturbations. SIAM Journal on Optimization, 18(3):717-732.

Abstract

This paper is concerned with the Lipschitzian behavior of the optimal set of convex semi-infinite optimization problems under continuous perturbations of the right hand side of the constraints and linear perturbations of the objective function. In this framework we provide a
sufficient condition for the metric regularity of the inverse of the optimal set mapping. This condition consists of the Slater constraint qualification, together with a certain additional requirement in the Karush-Kuhn-Tucker conditions. For linear problems this sufficient condition turns out to be also necessary for the metric regularity, and it is equivalent to some well-known stability concepts.

Abstract

This paper is concerned with the Lipschitzian behavior of the optimal set of convex semi-infinite optimization problems under continuous perturbations of the right hand side of the constraints and linear perturbations of the objective function. In this framework we provide a
sufficient condition for the metric regularity of the inverse of the optimal set mapping. This condition consists of the Slater constraint qualification, together with a certain additional requirement in the Karush-Kuhn-Tucker conditions. For linear problems this sufficient condition turns out to be also necessary for the metric regularity, and it is equivalent to some well-known stability concepts.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
Language:English
Date:2007
Deposited On:29 Jan 2009 09:52
Last Modified:21 Nov 2017 13:52
Publisher:Society for Industrial and Applied Mathematics
ISSN:1052-6234
Additional Information:Copyright © 2007, Society for Industrial and Applied Mathematics
Publisher DOI:https://doi.org/10.1137/060658345
Related URLs:http://search.ebscohost.com/login.aspx?direct=true&db=buh&AN=27827221&loginpage=Login.asp&site=ehost-live

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