Dual Characterization and Scalarization for Benson Proper Efficiency

By using dual cones and their properties, we establish a fundamental dual characterization and scalarization for Benson proper efficient points without any additional assumption on the ordering cone. From this, we obtain several scalarization theorems and Lagrange multiplier theorems for Benson proper minimizers of optimization problems with nearly cone-subconvexlike set-valued maps. The related known results are improved, and some new criteria for checking Benson proper efficiency are deduced.