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Second-order and stability analysis for state-constrained elliptic optimal control problems with sparse controls

Abstract: 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 L1-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 L2-regularization parameter for the control. The associated convergence rate is estimated.

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Autoría: Casas E., Troltzsch F.,

Fuente: SIAM Journal on Control and Optimization, 2014, 52(2), 1010–1033

Editorial: Society for Industrial and Applied Mathematics

Año de publicación: 2014

Nº de páginas: 24

Tipo de publicación: Artículo de Revista

DOI: 10.1137/130917314

ISSN: 0363-0129,1095-7138

Proyecto español: MTM2011-22711

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Autoría

EDUARDO CASAS RENTERIA

FREDI TRÖLTZSCH

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