Perturbing the Dual Feasible Region for Solving Convex Quadratic Programs

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.