A neurodynamic optimization technique based on overestimator and underestimator functions for solving a class of non-convex optimization problems

Abstract

In this paper, a novel neural network model for solving non-convex quadratic optimization problem is proposed. It is proved that the equilibrium points of the neural network model coincides with the local and global optimal solutions of the constrained non-convex optimization problem. Furthermore, it is shown that under suitable assumptions this model is globally convergent and stable in the sense of Lyapunov at each equilibrium points. Moreover a sufficient global optimality for non-convex non-quadratic objective function subject to a quadratic constraint is presented based on the corresponding underestimator function. Then for solving a class of non-convex optimization problems a novel neurodynamic optimization technique based on the necessary and sufficient global optimality is proposed. Both theoretical and numerical approaches are considered. Numerical simulations for several different non-convex quadratic optimization problems are discussed to illustrate great agreement between the theoretical and numerical results. The efficiency of the proposed neural network model is illustrated by numerical simulations and comparisons with available literature models.