Issue |
RAIRO-Oper. Res.
Volume 58, Number 5, September-October 2024
|
|
---|---|---|
Page(s) | 4259 - 4276 | |
DOI | https://doi.org/10.1051/ro/2024157 | |
Published online | 14 October 2024 |
First and second order necessary optimality conditions for multiobjective programming with interval-valued objective functions on Riemannian manifolds
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, Uttar Pradesh, India
* Corresponding author: akhlad6star@gmail.com; akhlad.mm@amu.ac.in
Received:
1
March
2024
Accepted:
24
July
2024
The growing dependence on optimization models in decision-making has created a demand for tools that can facilitate the formulation and resolution of a broader range of real-world processes and systems associated with human activity. These situations often involve assumptions that diverge from traditional optimization methodologies. One viable approach for addressing optimization problems in real-life scenarios with uncertainty is interval-valued optimization. Taking into account the significance of interval-valued optimization, in this paper, we derive first and second order necessary optimality conditions for a multi-objective programming problem with interval-valued objective functions defined on a Riemannian manifold. To establish these conditions, we consider the objective functions to be weakly differentiable and twice weakly differentiable for first and second order, respectively. Additionally, we assume that the constraints, both equality and inequality constraints, are differentiable and twice differentiable for first and second order conditions respectively. The first order as well as second order necessary conditions are derived under two types of constraint qualifications. Furthermore, we provide illustrative examples to demonstrate the application of the established results.
Mathematics Subject Classification: 90C25 / 90C29 / 90C30 / 90C46 / 90C70
Key words: Multi-objective programming problem / interval-valued function / first and second order necessary optimality conditions / constraint qualifications / KKT optimality conditions / Riemannian manifold
© 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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.