Constrained optimization based on gradient projection method and stochastic optimization algorithm

For the optimization problem with the unspecific function, linear equality and inequality constraints, a method which combines gradient projection method with stochastic approximation algorithm is proposed. The proposed method uses genetic algorithm(GA) to search the optimal solution overall the feasible region, and uses simultaneous perturbation stochastic approximation algorithm(SPSA) to search the optimal solution at the local region. During the search process, the proposed method generates a new individual along the gradient projection direction which is calculated according to linear equality and inequality constraints at father individual location, which ensures the new individual satisfy all constraints strictly. The proposed method is applied to three typical optimization problems, and the simulation results show the feasibility and convergence of the proposed method.