Osmolovskii, N. P., & Veliov, V. (2022). On the strong metric subregularity in mathematical programming. Control and Cybernetics, 50(4), 457–471. https://doi.org/10.2478/candc-2021-0027
This note presents sufficient conditions for the property of strong metric subregularity (SMSr) of the system of first order optimality conditions for a mathematical programming problem in a Banach space (the Karush-Kuhn-Tucker conditions). The constraints of the problem consist of equations in a Banach space setting and a finite number of inequalities. The conditions, under which SMSr is proven, assume that the data are twice continuously Fréchet differentiable, the strict Mangasarian-Fromovitz constraint qualification is satisfied, and the second-order sufficient optimality condition holds. The obtained result extends the one known for finite-dimensional problems. Although the applicability of the result is limited to the Banach space setting (due to the twice Fréchet differentiability assumptions and the finite number of inequality con-straints), the paper can be valuable due to the self-contained expo-sition, and provides a ground for extensions. One possible extension was recently implemented in Osmolovskii and Veliov (2021).
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Project title:
Optimale Steuerung mit endlichen Steuerungsmengen und Anwendungen in der Modelbasierten Regelung: P 31400-N32 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
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Research Areas:
Mathematical and Algorithmic Foundations: 20% Fundamental Mathematics Research: 80%
