Sparse optimal control of a quasilinear elliptic PDE in measure spaces

IF 1 4区数学 Q1 MATHEMATICS

Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI:10.3934/mcrf.2022049

Fabian Hoppe

引用次数: 0

Abstract

We prove existence of optimal controls for sparse optimal control of a quasilinear elliptic equation in measure spaces and derive first-order necessary optimality conditions. Under additional assumptions also second-order necessary and sufficient optimality conditions are obtained.

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测度空间中拟线性椭圆偏微分方程的稀疏最优控制

证明了拟线性椭圆型方程的稀疏最优控制在测度空间中的存在性，并导出了一阶必要最优性条件。在附加的假设条件下，还得到了二阶充分必要最优性条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Control and Related Fields MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

8.30%

发文量

期刊介绍： MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.