Global optimization by searching multiple equilibrium points of gradient dynamical system

This paper proposes a global optimization method based on searching for multiple equilibrium points of gradient-based dynamical systems. We are motivated to construct the method with significant mathematical properties of gradient systems from the viewpoint of optimization and nonlinear science. As the essence of this study, we propose a computational procedure for finding equilibrium points of nonlinear dynamical system with ascending or descending trajectories. The computation requires to generate trajectories from known equilibrium points to various directions. In this paper, we will further discuss the simplification of the procedure to reduce calculation by using a certain set of vectors. We will also show the effectiveness of our method through numerical simulations.