Second-Order and Stability Analysis for State-Constrained Elliptic Optimal Control Problems with Sparse Controls

An optimal control problem for a semilinear elliptic partial differential equation is discussed subject to pointwise control constraints on the control and the state. The main novelty of the paper is the presence of the $L^1$-norm of the control as part of the objective functional that eventually le...

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Bibliographic Details
Published inSIAM journal on control and optimization Vol. 52; no. 2; pp. 1010 - 1033
Main Authors Casas, Eduardo, Tröltzsch, Fredi
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2014
Subjects
Sparsity
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ISSN0363-0129
1095-7138
DOI10.1137/130917314

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Summary:An optimal control problem for a semilinear elliptic partial differential equation is discussed subject to pointwise control constraints on the control and the state. The main novelty of the paper is the presence of the $L^1$-norm of the control as part of the objective functional that eventually leads to sparsity of the optimal control functions. Second-order sufficient optimality conditions are analyzed. They are applied to show the convergence of optimal solutions for vanishing $L^2$-regularization parameter for the control. The associated convergence rate is estimated. [PUBLICATION ABSTRACT]
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ISSN:0363-0129
1095-7138
DOI:10.1137/130917314