Issue |
RAIRO-Oper. Res.
Volume 58, Number 4, July-August 2024
|
|
---|---|---|
Page(s) | 2817 - 2844 | |
DOI | https://doi.org/10.1051/ro/2024096 | |
Published online | 15 July 2024 |
Characterizations of the solution set of nonsmooth semi-infinite programming problems on Hadamard manifolds
Department of Mathematics, Indian Institute of Technology Patna, Patna, India
* Corresponding author: bhooshan@iitp.ac.in
Received:
5
June
2023
Accepted:
26
April
2024
This article is concerned with a class of nonsmooth semi-infinite programming problems on Hadamard manifolds (abbreviated as, (NSIP)). We introduce the Guignard constraint qualification (abbreviated as, (GCQ)) for (NSIP). Subsequently, by employing (GCQ), we establish the Karush-Kuhn-Tucker (abbreviated as, KKT) type necessary optimality conditions for (NSIP). Further, we derive that the Lagrangian function associated with a fixed Lagrange multiplier, corresponding to a known solution, remains constant on the solution set of (NSIP) under geodesic pseudoconvexity assumptions. Moreover, we derive certain characterizations of the solution set of the considered problem (NSIP) in the framework of Hadamard manifolds. We provide illustrative examples that highlight the importance of our established results. To the best of our knowledge, characterizations of the solution set of (NSIP) using Clarke subdifferentials on Hadamard manifolds have not been investigated before.
Mathematics Subject Classification: 90C34 / 90C46 / 90C48
Key words: Semi-infinite programming / geodesic pseudoconvexity / guignard constraint qualification / clarke subdifferential / hadamard manifolds
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024
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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