| Abstract: | This paper was motivated by an article by Best and Chakravarti, who presented some stability results for convex quadratic programs under linear perturbation of the data. We show that the regularity conditions assumed are much too restrictive and demonstrate that stronger stability results follow under weaker assumptions (primal solution boundedness and the Slater condition) and from known results, not only for convex quadratic problems but for general convex programs with general perturbations. In so doing, we give a simple and reasonably complete characterization of the stability of an important class of well-behaved convex programs, collecting results that heretofore have apparently not been presented in a unified manner. The results, virtually all from Hogan and Robinson, involve mainly stability of the feasible region and solution existence under small perturbations, and continuity and differentiability of the optimal value function. We note that Auslender and Coutat have recently provided similar extensions for saddle points of generalized linear-quadratic programs introduced by Rockafellar and Wets, utilizing the same assumptions that we use in this paper |
