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SIAM J. on Optimization / Volume 17 / Issue 1

SIAM J. Optim. 17, pp. 147-158 (12 pages)

On the Stability of Convex-valued Mappings and Their Relative Boundary and Extreme Points Set Mappings

Miguel A. Goberna, Maxim I. Todorov, and Virginia N. Vera de Serio

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This paper deals with the transmission of the main stability properties (lower and upper semicontinuity in Berge sense, and closedness) from a given closed--convex-valued mapping to its corresponding relative boundary and extreme point set mappings, and vice versa. The domain of the mappings considered in this paper are locally metrizable spaces and the images range on Euclidean spaces. Important examples of the class of mappings considered in this paper are the feasible set mapping and the optimal set mapping of convex optimization problems, for which the space of parameters is the result of perturbing a given nominal problem.

© 2006 Society for Industrial and Applied Mathematics

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AMS Subject Headings

49K40, 28B20

PUBLICATION DATA

ISSN

1052-6234 (print)  
1095-7189 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1137/050632476

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