Analysis of Optimal Control Problems of Semilinear Elliptic Equations by BV-Functions

被引：5

作者：

Casas, Eduardo ^{[1
]}

Kunisch, Karl ^{[2
]}

机构：

[1] Univ Cantabria, Dept Matemat Aplicada & Ciencias Comp, ETSI Ind & Telecomunicac, E-39005 Santander, Spain

[2] Karl Franzens Univ Graz, Inst Math & Sci Comp, Heinrichstr 36, A-8010 Graz, Austria

来源：

SET-VALUED AND VARIATIONAL ANALYSIS | 2019年 / 27卷 / 02期

基金：

欧盟地平线“2020”;

关键词：

Optimal control; Bounded variation functions; Sparsity; First and second order optimality conditions; Semilinear elliptic equations;

D O I：

10.1007/s11228-018-0482-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Optimal control problems for semilinear elliptic equations with control costs in the space of bounded variations are analysed. BV-based optimal controls favor piecewise constant, and hence 'simple' controls, with few jumps. Existence of optimal controls, necessary and sufficient optimality conditions of first and second order are analysed. Special attention is paid on the effect of the choice of the vector norm in the definition of the BV-seminorm for the optimal primal and adjoined variables.

引用

页码：355 / 379

页数：25

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