<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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 constraints), the paper can be valuable due to the self-contained exposition, and provides a ground for extensions. One possible extension was recently implemented in Osmolovskii and Veliov (2021).</p>
</abstract>

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 constraints), the paper can be valuable due to the self-contained exposition, and provides a ground for extensions. One possible extension was recently implemented in Osmolovskii and Veliov (2021).

On the strong metric subregularity in mathematical programming

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On the strong metric subregularity in mathematical programming"}

This note presents sufficient conditions for the property of strong metric subregularity (SMSr) of the system of first order optimality conditions for a...

On the strong metric subregularity in mathematical programming

Published Online: Jun 27, 2022

Page range: 457 - 471

Received: May 01, 2021

Accepted: Sep 01, 2021

DOI: https://doi.org/10.2478/candc-2021-0027

Keywords
optimization, mathematical programming, Karush-Kuhn-Tucker conditions, metric regularity

© 2021 Nikolai P. Osmolovskii et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the strong metric subregularity in mathematical programming

Published Online: Jun 27, 2022

Page range: 457 - 471

Received: May 01, 2021

Accepted: Sep 01, 2021

DOI: https://doi.org/10.2478/candc-2021-0027

Keywordsoptimization, mathematical programming, Karush-Kuhn-Tucker conditions, metric regularity

© 2021 Nikolai P. Osmolovskii et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
optimization, mathematical programming, Karush-Kuhn-Tucker conditions, metric regularity