Locally Lipschitz Stability of a Parametric Semilinear Elliptic Optimal Control Problem with Mixed Constraints

Quoc Tuan Nguyen ()
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Quoc Tuan Nguyen: Vietnam Academy of Science and Technology

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 3, No 4, 939-965

Abstract: Abstract This paper is concerned with the stability of minimizers to a parametric optimal control problem governed by semilinear elliptic equations with mixed pointwise control-state constraints. Under the strictly nonnegative second-order optimality condition assumption, we show that the solution map is locally Lipschitz continuous in $$L^2-$$ L 2 - norm as well as in $$L^\infty -$$ L ∞ - norm of the control variable.

Keywords: Solution stability; Locally Lipschitz upper continuity; Optimality condition; Second-order Sufficient optimality condition.; 49K15; 90C29 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02226-z

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