A diagonal finite element-projection-proximal gradient algorithm for elliptic optimal control problem

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...

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Bibliographic Details
Published in:	Computers & mathematics with applications (1987) Vol. 148; pp. 256 - 268
Main Authors:	Lin, Jitong, Chen, Xuesong
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 15.10.2023
Subjects:	Accelerated method Convergence analysis Finite element method Optimal control problem Proximal gradient algorithm Finite element method Proximal gradient algorithm Optimal control problem Accelerated method Convergence analysis
ISSN:	0898-1221, 1873-7668
Online Access:	Get full text
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Summary:	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.
ISSN:	0898-1221 1873-7668
DOI:	10.1016/j.camwa.2023.08.015