Lagrangian Multipliers, Saddle Points, and Duality in Vector Optimization of Set-Valued Maps

This paper establishes an alternative theorem for generalized inequality-equality systems of set-valued maps. Based on this, several (Lagrange) multiplier type as well as saddle point type necessary and sufficient conditions are obtained for the existence of weak minimizers in vector optimization of set-valued maps. Lagrange type duality theorems are also derived.