Optimal control problems with $$L^0(\Omega )$$ L 0 ( Ω ) constraints: maximum principle and proximal gradient method

Daniel Wachsmuth ()
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Daniel Wachsmuth: Universität Würzburg

Computational Optimization and Applications, 2024, vol. 87, issue 3, No 6, 833 pages

Abstract: Abstract We investigate optimal control problems with $$L^0$$ L 0 constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation is used that respects the $$L^0$$ L 0 constraint. First, the maximum principle is obtained in integral form, which is then turned into a pointwise form. In addition, an optimization algorithm of proximal gradient type is analyzed. Under some assumptions, the sequence of iterates contains strongly converging subsequences, whose limits are feasible and satisfy a subset of the necessary optimality conditions.

Keywords: Sparse optimal control; $$L^0$$ L 0 constraints; Pontryagin maximum principle; Proximal gradient method; 49M20; 49K20 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-023-00456-5

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