# Interval Valued Vector Variational Inequalities and Vector Optimization Problems via Convexificators

## TL;DR

This paper explores interval-valued vector optimization problems and their connection to vector variational inequalities using convexificators, extending existing theoretical results and analyzing LU-efficient solutions.

## Contribution

It introduces new relationships between interval vector variational inequalities and LU-efficient solutions via convexificators, including weak versions and generalizations.

## Key findings

- Established links between IVOP and IVVI using convexificators.
- Extended existing results to weak versions of variational inequalities.
- Provided generalized conditions for LU-efficient solutions.

## Abstract

In this paper, we consider interval-valued vector optimization problems $(IVOP)$ and derive their relationships to interval vector variational inequalities $(IVVI)$ of Minty and Stampacchia type in terms of convexificators and LU-efficient solution of $(IVOP)$ using LU-convexity assumption. Furthermore, we consider weak versions of $(IVVI)$ of Minty and Stampacchia type and find the relationships between weak versions of $(IVVI)$ of Minty and Stampacchia type and weakly LU-efficient solution of $(IVOP)$. The results presented in this paper extend and generalized some existing results in the literature.