A global convergent semi-smooth Newton method for semi-linear elliptic optimal control problem
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DOI码：10.1016/j.camwa.2022.06.013
发表刊物：Computers & Mathematics with Applications
关键字：Optimal control; Optimality conditions; Semismooth Newton; Semi-linear elliptic equation; Nonmonotone convergence
摘要：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.
第一作者：Zemian Zhang
论文类型：期刊论文
通讯作者：Xuesong Chen
卷号：120:
页面范围：15-27
是否译文：否
发表时间：2022-08-15
收录刊物：SCI
发布期刊链接：https://doi.org/10.1016/j.camwa.2022.06.013
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