FIRST AND SECOND ORDER CONDITIONS FOR OPTIMAL CONTROL PROBLEMS WITH AN L0 TERM IN THE COST FUNCTIONAL

被引：5
|
作者：
Casas, Eduardo [1 ]
Wachsmuth, Daniel [2 ]
机构：
[1] Univ Cantabria, Dept Matemat Aplicada & Ciencias Comp ETSI & Ind, Santander 39005, Spain
[2] Univ Wurzburg, Inst Math, D-97074 Wurzburg, Germany
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2020年 / 58卷 / 06期
关键词：
optimal control; semilinear partial differential equation; optimality conditions; sparse controls; BANG CONTROL;
D O I：
10.1137/20M1318377
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equation. The cost functional contains a term that measures the size of the support of the control, which is the so-called L-0-norm. We provide necessary and sufficient optimality conditions of second order. The sufficient second-order condition is obtained by analyzing a partially convexified problem. Interestingly, the structure of the problem yields second-order conditions with different bilinear forms for the necessary and for the sufficient conditions.
引用
收藏
页码：3486 / 3507
页数：22
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