Some results on directionally differentiable multicriteria interval-valued optimization problems with vanishing constraints

Murari Kumar Roy; Bhuwan Chandra Joshi; Satya Jeet Singh; Abdelouahed Hamdi; Murari Kumar Roy; Bhuwan Chandra Joshi; Satya Jeet Singh; Abdelouahed Hamdi

doi:10.3934/jimo.2026029

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 2: 806-831. doi: 10.3934/jimo.2026029

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Research article

Some results on directionally differentiable multicriteria interval-valued optimization problems with vanishing constraints

1.
Department of Mathematics, Graphic Era (Deemed to Be University), Dehradun 248002, India
2.
Department of Mathematics, School of Advanced Engineering, UPES, Dehradun 248007, India
3.
Mathematics Program, Department of Mathematics and Statistics, College of Arts and Sciences, Qatar University, Doha P.O. Box 2713, Qatar

Received: 01 May 2025 Revised: 06 October 2025 Accepted: 13 November 2025 Published: 04 January 2026
90C46, 90C30, 49J52

In this article, we examine the theoretical properties of interval-valued multiobjective optimization problems that are directionally differentiable and include equality, inequality, and vanishing constraints. The objective functions in these problems are considered interval-valued. Necessary conditions for optimality in nondifferentiable multiobjective optimization are derived under the Abadie and a modified Abadie constraint qualification. Furthermore, sufficient optimality conditions are proven under appropriate convexity assumptions. A Numerical example is also presented to validate the theoretical results of this work.
- pareto solution,
- directionally differentiable multiobjective optimization problems,
- interval valued functions
Citation: Murari Kumar Roy, Bhuwan Chandra Joshi, Satya Jeet Singh, Abdelouahed Hamdi. Some results on directionally differentiable multicriteria interval-valued optimization problems with vanishing constraints[J]. Journal of Industrial and Management Optimization, 2026, 22(2): 806-831. doi: 10.3934/jimo.2026029

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Abstract

In this article, we examine the theoretical properties of interval-valued multiobjective optimization problems that are directionally differentiable and include equality, inequality, and vanishing constraints. The objective functions in these problems are considered interval-valued. Necessary conditions for optimality in nondifferentiable multiobjective optimization are derived under the Abadie and a modified Abadie constraint qualification. Furthermore, sufficient optimality conditions are proven under appropriate convexity assumptions. A Numerical example is also presented to validate the theoretical results of this work.

References

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