We discuss conditions for the Aubin property of solutions to perturbed cone constrained programs, by using and refining results given in Klatte and Kummer (Nonsmooth equations in optimization. Kluwer, Dordrecht, <CitationRef CitationID="CR10">2002</CitationRef>). In particular, we show that constraint nondegeneracy and hence uniqueness of...</citationref>

In this paper we study the (Berge) upper semicontinuity of a generic multifunction assigning to each parameter, in a metric space, a closed convex subset of the n-dimensional Euclidean space. A relevant particular case arises when we consider the feasible set mapping associated with a parametric...

This article studies continuity and directional differentiability properties of optimal value functions, in particular at boundary points of their domain. We extend and complement standard continuity results from Hogan (SIAM Rev 15:591–603, <CitationRef CitationID="CR12">1973a</CitationRef>) for abstract feasible set mappings under...</citationref>

We discuss in this paper statistical inference of sample average approximations of multistage stochastic programming problems. We show that any random sampling scheme provides a valid statistical lower bound for the optimal (minimum) value of the true problem. However, in order for such lower...

We take advantage of the interpretation of stochastic capacity expansion problems as stochastic equilibrium models for assessing the risk exposure of new equipment in a competitive electricity economy. We develop our analysis on a standard multistage generation capacity expansion problem. We...