A diagonal finite element-projection-proximal gradient algorithm for elliptic optimal control problem - Lin, Jitong; Chen, Xuesong (Computers & mathematics with applications (1987), 2023)
A diagonal finite element-projection-proximal gradient (DFE-P-PG) algorithm and its accelerated forms for elliptic optimal control problem with L1-control cost are proposed in this paper. Firstly, the elliptic optimal control problem is discretized by the diagonal finite element method (DFEM). Then the discrete problem is optimized by projection-proximal gradient (P-PG) algorithm. The global convergence of DFE-P-PG algorithm is proven. In addition, two accelerated methods are used to enhance the convergence rate of DFE-P-PG algorithm. Numerical examples are performed to illustrate the efficiency and effectiveness of DFE-P-PG algorithm. •A diagonal finite element-projection-proximal gradient algorithm for elliptic optimal control problem is proposed.•We use two accelerated schemes to improve the convergence rate of finite element-projection-proximal gradient algorithm.•The convergence properties of algorithms are proven theoretically.