| Issue |
RAIRO-Oper. Res.
Volume 57, Number 5, September-October 2023
|
|
|---|---|---|
| Page(s) | 2687 - 2702 | |
| DOI | https://doi.org/10.1051/ro/2023123 | |
| Published online | 20 October 2023 | |
Strongly geodesic preinvexity and strongly invariant η-monotonicity on Riemannian manifolds and its application
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
* Corresponding author: askarhussain59@gmail.com
Received:
4
February
2023
Accepted:
19
August
2023
This paper introduces the concepts of strongly geodesic preinvexity, strongly η-invexity of order m, and strongly invariant η-monotonicity of order m on Riemannian manifolds. Additionally, it discusses an important characterization of these functions under a condition, known as Condition C (The Condition C is defined in Remark 1 of this article), defined by Barani and Pouryayevali [J. Math. Anal. Appl. 328 (2007) 767–779]. The paper provides various non-trivial examples to support these definitions. Furthermore, it presents a significant characterization of strict η-minimizers (or η-minimizers) of order m for multi-objective optimization problems and a solution to the vector variational-like inequality problem.
Mathematics Subject Classification: 26B25 / 26D07 / 90C25
Key words: Strongly geodesic preinvexity / strongly η-invex functions / invariant η-monotone vector fields / multi-objective optimization problem / vector variational like-inequality problem / Riemannian manifolds
© 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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