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arXiv · 2309.05393

Convergence analysis of the semismooth Newton method for sparse control problems governed by semilinear elliptic equations

Casas Eduardo·Mateos Mariano
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Abstract

We show that a second order sufficient condition for local optimality, along with a strict complementarity condition, is enough to get the superlinear convergence of the semismooth Newton method for an optimal control problem governed by a semilinear elliptic equation. The objective functional may include a sparsity promoting term and we allow for box control constraints.

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Casas Eduardo, Mateos Mariano. 2023-09-11. Convergence analysis of the semismooth Newton method for sparse control problems governed by semilinear elliptic equations. https://doi.org/10.1137/23m1585945

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