Conic scalarizations for approximate efficient solutions in nonconvex vector optimization problems
This paper develops a method to characterize approximate efficient/ weakly efficients and properly efficient points of a set with respect to an improvemennt set. The main tool is the nonlinear scalarization by the functions of the form \(\sup_{y\in -E} ( \langle y^\ast, y\rangle +\alpha \| y\|)\) and \(\inf_{y\in E} ( \langle y^\ast, y\rangle +\alpha \| y\|)\), where \(E\) is the improvement set, \((y^\ast, \alpha)\) is chosen from the augmented dual cones of the ordering cone. The authors present also a correction to a scalarization result in [\textit{R. N. Gasimov}, Lect. Notes Econ. Math. Syst. 507, 189--198 (2001; Zbl 1014.90087)] when the Bishop-Phelps cone is used.
scientific article; zbMATH DE number 6841405