A direct search algorithm based on kernel density estimator for nonlinear optimization

In this paper, we propose a direct search algorithm based on kernel density estimator for the nonlinear optimization problems. It estimates the objective function by the kernel density estimator with the local samples only, and then approximates the ascent direction of the objective function with the one of the estimator. The proposed optimization approach features the derivative-free with much likely generating an ascent direction. We not only theoretically show that the search direction, which is used in the proposed algorithm towards maximizing the objective function, is the ascent direction of the objective function, but also empirically investigate the effectiveness of the search direction.