Scalarizations and Lagrange multipliers for approximate solutions in the vector optimization problems with set-valued maps
Ying Gao, Xinmin Yang, Jin Yang, Hong Yan · Journal of Industrial and Management Optimization · 2014
In this paper, we characterize approximate solutions of vector optimization problems with set-valued maps. We gives several characterizations of generalized subconvexlike set-valued functions(see [10]), which is a generalization of nearly subconvexlikefunctions introduced in [34]. We present alternative theoremand derived scalarization theorems for approximate solutions with generalizedsubconvexlike set-valued maps. And then, Lagrange multipliertheorems under generalized Slater constraint qualification areestablished.