A study on vector variational-like inequalities using convexificators and application to its bi-level form

Abstract

<p style='text-indent:20px;'>This paper deals with the weak versions of the vector variational-like inequalities, namely Stampacchia and Minty type under invexity in the framework of convexificators. The connection between both the problems along with the link to vector optimization problem are analyzed. An application to nonconvex mathematical programming has also been presented. Further, the bi-level version of these problems is formulated and a procedure to obtain the solution involving the auxiliary principle technique is described in detail. We have shown that the iterative algorithm with the help of which we get the approximate solution converges strongly to the exact solution of the problem.</p>