On Approximate Solutions for Nonsmooth Interval-Valued Multiobjective Optimization Problems with Vanishing Constraints

The purpose of this research is to develop approximate weak and strong stationary conditions for interval-valued multiobjective optimization problems with vanishing constraints (IVMOPVC) involving nonsmooth functions. In many real-world situations, the exact values of objectives are uncertain or imp...

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Vydáno v:Mathematics (Basel) Ročník 13; číslo 22; s. 3699
Hlavní autoři: Dwivedi, Akriti, Laha, Vivek, Beldiman, Miruna-Mihaela, Halanay, Andrei-Dan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.11.2025
Témata:
approximate constraint qualifications
approximate efficient solutions
approximate stationary conditions
Approximation
Constraints
Convexity
interval-valued multiobjective optimization
Linear programming
Mathematical programming
Multiple objective analysis
Optimization
Pareto optimization
Qualifications
Regularization methods
vanishing constraints
ISSN:2227-7390, 2227-7390
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Shrnutí:The purpose of this research is to develop approximate weak and strong stationary conditions for interval-valued multiobjective optimization problems with vanishing constraints (IVMOPVC) involving nonsmooth functions. In many real-world situations, the exact values of objectives are uncertain or imprecise; hence, interval-valued formulations are used to model such uncertainty more effectively. The proposed approximate weak and strong stationarity conditions provide a robust framework for deriving meaningful optimality results even when the usual constraint and data qualifications fail. We first introduce approximate variants of these qualifications and establish their relationships. Secondly, we establish some approximate KKT type necessary optimality conditions in terms of approximate weak strongly stationary points and approximate strong strongly stationary points to identify type-2 E-quasi weakly Pareto and type-1 E-quasi Pareto solutions of the IVMOPVC. Lastly, we show that the approximate weak and strong strongly stationary conditions are sufficient for optimality under some approximate convexity assumptions. All the outcomes are well illustrated by examples.
Bibliografie:ObjectType-Article-1
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ISSN:2227-7390
2227-7390
DOI:10.3390/math13223699