Directional optimality conditions for multiobjective program constrained by parameterized variational inequalities

In this paper, we discuss the multiobjective program constrained by parameterized variational inequalities. By employing the directional limiting coderivative, which depicts the local behavior of set -valued mappings along relevant directions, a weaker constraint qualification condition is imposed on the optimization problem. Under the metric subregularity constraint qualification of constraint functions and some assumptions on the problem data, the calculus for the directional limiting coderivatives of investigated set-valued mappings is obtained. With the weaker constraint qualification condition, the directionally necessary condition for the multiobjective program with respect to the critical direction is established.