Variational Inequalities Characterizing Weak Minimality in Set Optimization
We introduce the notion of weak minimizer in set optimization. Necessary and sufficient conditions in terms of scalarized variational inequalities of Stampacchia and Minty type, respectively, are proved. As an application, we obtain necessary and sufficient optimality conditions for weak efficiency of vector optimization in infinite-dimensional spaces. A Minty variational principle in this framework is proved as a corollary of our main result.
variational inequalities set optimization scalarization weak efficiency 49j40 49j53 58c06 58e30