Stabilization and determination of the set of minimal binding constraints in convex programming1

Abstract

Every convex program can be rewritten as a stable program after identifying the minimal index set of binding constraints. This paper suggests a finite iterative method for calculating this particular set of indices. The method is demonstrated on such diverse problems as characterizing a PABETG optimum in multicriteria optimization and solving differentiable convex programs by the method of augmented Lagrangians without assuming a regularization condition. Some results extend to arbitrary convex cones and abstract spaces, and apply to optimal control problems.