Nonlinear scalarization approaches for characterizing E -efficiency classes in nonconvex vector optimization

In this paper, we first summarize the mutual inclusion relations among four classes of efficient points defined via an improvement set E, namely E-strictly efficient points, E-super efficient points, E-globally properly efficient points, and E-Henig properly efficient points. Then, in reflexive Banach spaces, we establish new nonlinear scalarization theorems for characterizing these efficient points in nonconvex vector optimization by means of monotone normlinear functions generated via augmented dual cones. Based on Kasimbeyli's nonlinear separation theorem (see, Kasimbeyli [SIAM J. Optim., 20 (2010), pp. 1591–1619]) for nonconvex cones, we derive sufficient and necessary scalarization conditions without convexity assumptions and show that these efficiency notions can be characterized through the minimization of explicitly constructed sublinear functionals. These results extend nonlinear scalarization theory and provide a unified framework for analysing classes of E-efficiency in nonconvex settings.