Goberna, Miguel A., Todorov, Maxim I., Vera de Serio, Virginia N.
On the stability of convex-valued mappings and their relative boundary and extreme point set mappings
GOBERNA TORRENT, Miguel Ángel; TODOROV, Maxim I.; VERA DE SERIO, Virginia N. "On the stability of convex-valued mappings and their relative boundary and extreme point set mappings". SIAM Journal on Optimization. Vol. 17, No. 1 (2006). ISSN 1052-6234, pp. 147-158
URI: http://hdl.handle.net/10045/8151
DOI: 10.1137/050632476
ISSN: 1052-6234 (Print)
Abstract: 
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.
Keywords:Stability theory, Set-valued mappings, Convex hull mappings, Relative boundary mappings, Extreme points set mappings
Society for Industrial and Applied Mathematics
info:eu-repo/semantics/article