Stability of Minima in Constrained Optimization Problems and Implicit Function Theorem

Aram V. Arutyunov (), Kirill A. Tsarkov () and Sergey E. Zhukovskiy ()
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Aram V. Arutyunov: V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
Kirill A. Tsarkov: V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
Sergey E. Zhukovskiy: V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 2, No 9, 1293-1308

Abstract: Abstract In the paper, we consider both finite-dimensional and infinite-dimensional optimization problems with inclusion-type and equality-type constraints. We obtain sufficient conditions for the stability in the weak topology of a solution to this problem with respect to small perturbations of the problem parameters. In the finite-dimensional case, conditions for the stability in the strong topology of the solution are obtained for the problem with equality-type constraints. These conditions are based on a certain implicit function theorem.

Keywords: Stability of solutions; Constrained optimization; Parameterized extremal problem; Implicit function theorem; 46N10; 49K27; 49K40 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02459-6

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