On nonsmooth V-invexity and vector variational-like inequalities in terms of the Michel‐Penot subdifferentials

In this paper, we establish some results which exhibit an application for Michel–Penot subdifferential in nonsmooth vector optimization problems and vector variational‐like inequalities. We formulate vector variational‐like inequalities of Stampacchia and Minty type in terms of the Michel–Penot subdifferentials and use these variational‐like inequalities as a tool to solve the vector optimization problem involving nonsmooth V‐invex function. We also consider the corresponding weak versions of the vector variational‐like inequalities and establish various results for the weak efficient solutions.