A Neurogenetic Approach and its Application to Constrained Nonlinear Convex Optimization Problems with Joint and Disjoint Feasible Regions

A neurogenetic approach is presented for solving constrained nonlinear convex optimization problems with joint and disjoint feasible regions. More specifically, a modified Hopfield neural network is associated with a genetic algorithm in order to treat optimization and constraint terms in different stages with no interference with each other. Under the condition that the objective function is convex and the constraint set is convex, the proposed approach is proved to be stable in the sense of Lyapunov and globally convergent to the equilibrium points, which represent feasible solutions for constrained nonlinear convex optimization problems. Simulation results are provided to demonstrate the performance of the proposed approach.