On interval-valued vector variational-like inequalities and vector optimization problems with generalized approximate invexity via convexificators

In this paper, we establish the relationships between a class of interval-valued vector optimization problems and interval-valued vector variational-like inequality problems of both Stampacchia and Minty kinds in terms of convexificators. We also provide necessary and sufficient optimality requirements for locally strong quasi and approximately efficient solutions by using the concept of approximate LU-$ (\eta, e) $-invexity. Numerical example is also presented to validate the main result. Our newly proved results generalize some well-known results in the literature.