A fast gradient projection algorithm for time fractional optimal control problem

Abstract

In this paper a fast gradient projection algorithm for optimal control problems governed by time fractional diffusion equation is developed. The state equation is discretized by piecewise linear FE for space variable and L1 scheme for time variable, while the control variable is approximated by variational discretization. Based on the block triangular Toeplitz structure of the coefficient matrix of the discretized state equation and adjoint state equation, a fast gradient projection algorithm is designed for the control problem. Numerical examples are carried out to illustrate the effectiveness of the algorithms.