Error estimates for the approximation of multibang control problems

被引：1

作者：

Clason, Christian ^{[1
]}

Thi Bich Tram Do ^{[1
]}

Poerner, Frank ^{[2
]}

机构：

[1] Univ Duisburg Essen, Fac Math, D-45117 Essen, Germany

[2] Univ Wurzburg, Dept Math, Emil Fischer Str 40, D-97074 Wurzburg, Germany

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2018年 / 71卷 / 03期

关键词：

Multibang control; Moreau-Yosida approximation; Finite element discretization; Error estimates; Semi-smooth Newton method; CONVEX-ANALYSIS APPROACH; VARIATIONAL DISCRETIZATION; REGULARIZATION;

D O I：

10.1007/s10589-018-0026-y

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

This work is concerned with optimal control problems where the objective functional consists of a tracking-type functional and an additional "multibang" regularization functional that promotes optimal control taking values from a given discrete set pointwise almost everywhere. Under a regularity condition on the set where these discrete values are attained, error estimates for the Moreau-Yosida approximation (which allows its solution by a semismooth Newton method) and the discretization of the problem are derived. Numerical results support the theoretical findings.

引用

页码：857 / 878

页数：22

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