DOI number:10.1016/j.camwa.2023.08.015

Journal:Computers & Mathematics with Applications

Key Words:optimal control problem; finite element method; proximal gradient algorithm; accelerated method; convergence analysis

Abstract:A diagonal finite element-projection-proximal gradient (DFE-P-PG) algorithm and its accelerated forms for elliptic optimal control problem with $L^1$-control cost are proposed in this paper. Firstly, the elliptic optimal control problem is discretized by 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.

First Author:Jitong Lin

Indexed by:Journal paper

Correspondence Author:Xuesong Chen

Volume:148:

Page Number:256-268

Translation or Not:no

Date of Publication:2023-09-05

Included Journals:SCI

Links to published journals:https://authors.elsevier.com/a/1hiMG3CDPQ6qQ8