Estimates for Kuhn-Tucker points of perturbed convex programs

Abstract

For saddle points of perturbed convex-concave functions in finite dimensional space we give a quantitative characterization of upper semicontinuity. Specifying these results to the standard Lagrangian we obtain bounds for Kuhn-Tucker points of perturbed .convex programs without imposing differentiability of the problem functions. As a further application of the underlying techniques we present an estimate which relates the Hausdorff-distance of the graphs of the ∊-subdifferentials of convex, functions to the function distance with respect to the maximum norm.

Keywords:

• Nondifferentiable convex programming
• stability of Kuhn-Tucker points
• saddle point
• subdifferential

AMS 1980 Subject Classification:

• Primary:49 B 50
• Secondary:26 B 25