Notes on the convergence and applications of surrogate optimization

Abstract

Surrogate optimization is a computational procedure that uses a sequence of approximations of the objective function to predict an optimum. Even in the case when the derivative information of the objective function is not available, the surrogate functions can still be constructed only based on the function values. Moreover, the optimization method may provide required tools for computing the numerical solution of certain nonlinear differential equations in recent engineering applications, such as the optimal determination of the perturbation values in robot control dynamic systems [13, 16, 18]. In this paper, we will present a direct convergence analysis of the surrogate optimization process in one dimensional fashion via polynomial interpolations of objective function values. Numerical experiments will be given to illustrate the effectiveness of the algorithms developed. An application in multi-agent cooperative search problem will be also presented.