Solving a class of non-convex quadratic problems based on generalized KKT conditions and neurodynamic optimization technique

Abstract

In this paper, based on a generalized Karush-Kuhn-Tucker (KKT) method a modified recurrent neural network model for a class of non-convex quadratic programming problems involving a so-called $Z$-matrix is proposed. The basic idea is to express the optimality condition as a mixed nonlinear complementarity problem. Then one may specify conditions for guaranteeing the global solutions of the original problem by using results from the S-lemma. This process is proved by building up a dynamic system from the optimality condition whose equilibrium point is exactly the solution of the mixed nonlinear complementarity problem. By the study of the resulting dynamic system it is shown that under given assumptions, steady states of the dynamic system are stable. Numerical simulations and comparisons with the other methods are presented to illustrate the efficiency of the practical technique that is proposed in this paper.