| Issue |
RAIRO-Oper. Res.
Volume 57, Number 5, September-October 2023
|
|
|---|---|---|
| Page(s) | 2585 - 2600 | |
| DOI | https://doi.org/10.1051/ro/2023124 | |
| Published online | 09 October 2023 | |
On characterizations of solution sets of interval-valued quasiconvex programming problems
1
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, Uttar Pradesh, India
2
Department of Mathematics, V.S.S.D. College, Kanpur 208002, Uttar Pradesh, India
* Corresponding author: mohd.hassan10@bhu.ac.in
Received:
9
February
2023
Accepted:
12
August
2023
In this article, we study several characterizations of solution sets of LU-quasiconvex interval-valued function. Firstly, we provide Gordan’s theorem of the alternative of interval-valued linear system. As a consequence of this theorem, we find the normalized gradient of the interval-valued function is constant over the solution set when its gradient is not zero. Further, we discuss Lagrange multiplier characterizations of solution sets of LU-quasiconvex interval-valued function and provide optimality conditions of interval-valued optimization problem under the generalized Mangasarian-Fromovitz constraint qualifications. We provide illustrative examples in the support of our theory.
Mathematics Subject Classification: 26B25 / 90C46 / 65G40
Key words: Quasiconvex functions / interval-valued optimization problem / KKT optimality conditions
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
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