| Issue |
RAIRO-Oper. Res.
Volume 57, Number 5, September-October 2023
|
|
|---|---|---|
| Page(s) | 2721 - 2734 | |
| DOI | https://doi.org/10.1051/ro/2023138 | |
| Published online | 24 October 2023 | |
On Frèchet normal cone for nonsmooth mathematical programming problems with switching constraints
1
Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran
2
Department of Mathematics, Indian Institute of Technology Patna, Patna, India
* Corresponding author: bhooshan@iitp.ac.in
Received:
22
July
2023
Accepted:
4
September
2023
This paper is devoted to the study of a class of nonsmooth programming problems with switching constraints (abbreviated as, (NMPSC)), where all the involved functions in the switching constraints are assumed to be locally Lipschitz. We investigate the properties of Frèchet normal cone of (NMPSC). In particular, we introduce two Guignard type constraint qualifications for (NMPSC) in terms of Michel-Penot subdifferential. Moreover, we derive two estimates for the Frèchet normal cone of (NMPSC) and further establish stationarity conditions at an optimal solution for (NMPSC). To the best of our knowledge, this is for the first time Frèchet normal cone for (NMPSC) have been studied in the setting of Euclidean spaces.
Mathematics Subject Classification: 49J52 / 90C30 / 90C33 / 90C46
Key words: Guignard constraint qualification / stationary conditions / Michel-Penot subdifferential / switching constraints
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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