Constrained optimization using the chaotic Lagrangian method and the simultaneous perturbation gradient approximation

As one of the global optimization methods to solve constrained optimization problems, we have proposed a chaotic Lagrangian method which utilizes chaotic search trajectories generated in a coupled gradient dynamics with respect to the augmented Lagrangian. We have confirmed the global search capability of the chaotic Lagrangian method. However, the chaotic Lagrangian method cannot be applied to a class of problems whose objective function is indifferentiable, because the chaotic Lagrangian method uses the gradient as a driving force. In this study, we introduce the simultaneous perturbation gradient approximation into the chaotic Lagrangian method in order to compute the gradient approximately.