Perturbing the Dual Feasible Region for Solving Convex Quadratic Programs

Abstract

A dual l _p-norm perturbation approach is introduced for solving convex quadratic programming problems. The feasible region of the Lagrangian dual program is approximated by a proper subset that is defined by a single smooth convex constraint involving the l _p-norm of a vector measure of constraint violation. It is shown that the perturbed dual program becomes the dual program as p→∞ and, under some standard conditions, the optimal solution of the perturbed dual program converges to a dual optimal solution. A closed-form formula that converts an optimal solution of the perturbed dual program into a feasible solution of the primal convex quadratic program is also provided. Such primal feasible solutions converge to an optimal primal solution as p→∞. The proposed approach generalizes the previously proposed primal perturbation approach with an entropic barrier function. Its theory specializes easily for linear programming.