Stochastic perturbation of reduced gradient & GRG methods for nonconvex programming problems

In this paper, we consider nonconvex differentiable programming under linear and nonlinear differentiable constraints. A reduced gradient and GRG (generalized reduced gradient) descent methods involving stochastic perturbation are proposed and we give a mathematical result establishing the convergence to a global minimizer. Numerical examples are given in order to show that the method is effective to calculate. Namely, we consider classical tests such as the statistical problem, the octagon problem, the mixture problem and an application to the linear optimal control servomotor problem.