Sensitivity analysis for generalized linear-quadratic problems

In this paper, we study simple necessary and sufficient conditions for the stability of generalized linear-quadratic programs under perturbations of the data. The concept of generalized linear-quadratic problem was introduced by Rockafellar and Wets and consists of solving saddle points of a linear-quadratic convex concave function J on U x V, where U and V are polyhedral convex sets in R(n) and R(m). This paper also establishes results on the closedness and the uniform boundedness of the saddle-point solution sets. These properties are then used to obtain results on the continuity and the directional derivative of the perturbed saddle value.