The localized method of approximate particular solutions for solving an optimal control problem

Abstract

In this paper, we consider the localized method of approximate particular solutions (LMAPS) for solving a two-dimensional distributive optimal control problem governed by elliptic partial differential equations. Both radial basis functions and polynomial basis functions (RBFs) are used in the LMAPS discretization, while the leave-one-out cross-validation is adopted for the selection of the shape parameter appeared in RBFs. Numerical experiments are presented to demonstrate the accuracy and efficiency of the proposed method.