Akriti Dwivedi, Prachi Sachan, Vivek Laha, On an interval-valued multiobjective optimization problem and approximate vector variational inequalities in terms of directional convexificators
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DOI: 10.23952/jano.8.2026.2.08
Volume 8, Issue 2, 1 August 2026, Pages 295-317
Abstract. In this paper, we develop approximate vector variational inequalities of both Stampacchia and Minty types by using the concept of directional convexificators (DCs), and establish their connection to an interval-valued multiobjective optimization problem (IVMOP). Our method employs a form of approximate convexity defined through DCs to derive necessary and sufficient conditions for a point to qualify as an approximate Pareto efficient solution of the IVMOP. Additionally, we explore the weak formulations of these approximate variational inequalities and present several results aimed at identifying approximate weak Pareto efficient solutions. To illustrate our approach and highlight the limitations of some existing work, we include some detailed examples. Our results demonstrate that DCs offer a powerful and flexible approach for handling complex optimization problems with interval-valued objectives.
How to Cite this Article:
A. Dwivedi, P. Sachan, V. Laha, On an interval-valued multiobjective optimization problem and approximate vector variational inequalities in terms of directional convexificators, J. Appl. Numer. Optim. 8 (2026), 295-317.