Global optimization by random perturbation of the gradient method with a fixed parameter (Q1337130)

An objective function is supposed multimodal, bounded and differentiable, and a feasible region is a ball in Euclidean space. The algorithm is the implementation of a randomly perturbed gradient method. The perturbation is a random vector \(Z\) multiplied by the decreasing factor converging to zero where \(Z\) almost surely belongs to the feasible region. Convergence with probability 1 is proved. Results of experiments are reported.