DOI number:10.1016/j.camwa.2022.06.013

Journal:Computers & Mathematics with Applications

Key Words:Optimal control; Optimality conditions; Semismooth Newton; Semi-linear elliptic equation; Nonmonotone convergence

Abstract:Global convergent semi-smooth Newton (GCSSN) method for $L^2$-norm control constrained elliptic optimal control problem with $L^1$-control cost is discussed. The first order necessary optimality conditions is analyzed and reduced system is proposed. After finite difference discretization, we propose the global convergent semi-smooth Newton method for discrete reduced system with the nonmonotone line search. The local superlinear convergence rate and convergence are proved theoretically. The demonstrated theoretical properties are verified with numerical results. To illustrate the effectiveness and efficiency, we compare the proposed method with semi-smooth Newton method in the simulation part.

First Author:Zemian Zhang

Indexed by:Journal paper

Correspondence Author:Xuesong Chen

Volume:120:

Page Number:15-27

Translation or Not:no

Date of Publication:2022-08-15

Included Journals:SCI

Links to published journals:https://doi.org/10.1016/j.camwa.2022.06.013