Dinh, Nguyen, Goberna, Miguel A., López Cerdá, Marco A.
On the stability of the feasible set in optimization problems
DINH, Nguyen; GOBERNA TORRENT, Miguel Ángel; LÓPEZ CERDÁ, Marco Antonio. “On the stability of the feasible set in optimization problems”. SIAM Journal on Optimization. Vol. 20, No. 5 (2010). ISSN 1052-6234, pp. 2254-2280
URI: http://hdl.handle.net/10045/15406
DOI: 10.1137/090746331
ISSN: 1052-6234 (Print)
Abstract: 
This paper provides stability theorems for the feasible set of optimization problems posed in locally convex topological vector spaces. The problems considered in this paper have an arbitrary number of inequality constraints and one constraint set. Different models are discussed, depending on the properties of the constraint functions (linear or not, convex or not, but at least lower semicontinuous) and one closed constraint set (but not necessarily convex). The parameter space is formed by systems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the constraint set can be perturbed or not, equipped with the metric of the uniform convergence on the positive multiples of a fixed barrelled neighborhood of zero. In finite dimensions, this topology describes the uniform convergence on compact sets and, in the particular case that the constraints are linear, the uniform convergence of the vector coefficients. The paper examines, in a unified way, the lower and upper semicontinuity, and the closedness, of the feasible set mapping, the stable consistency of the constraint system with respect to arbitrary and right-hand side perturbations, Tuy and Robinson regularities, and other desirable stability properties of the feasible set.
Keywords:Feasible set, Stability, Infinite optimization, Semi-infinite optimization
Society for Industrial and Applied Mathematics
info:eu-repo/semantics/article