A canonical dual approach for solving linearly constrained quadratic programs

This paper provides a canonical dual approach for minimizing a general quadratic function over a set of linear constraints. We first perturb the feasible domain by a quadratic constraint, and then solve a “restricted” canonical dual program of the perturbed problem at each iteration to generate a sequence of feasible solutions of the original problem. The generated sequence is proven to be convergent to a Karush–Kuhn–Tucker point with a strictly decreasing objective value. Some numerical results are provided to illustrate the proposed approach.

► We develop an iterative scheme based on the canonical duality theory. ► A convex quadratic programming outputs a feasible solution at each iteration. ► The solution either provides a KKT point or generates a better feasible solution. ► The iterations of feasible points eventually converge to a KKT point. ► A global minimizer is possibly obtained by arbitrarily re-selecting an initial point.