Linear and Nonlinear Scalarization Methods for Vector Optimization Problems with Variable Ordering Structures
Jian-Wen Peng, Wenbin Wei, Refail Kasımbeyli · Journal of Optimization Theory and Applications · 2025
Abstract This paper investigates linear and nonlinear scalarization methods for vector optimization problems with variable ordering structures (VOS). Firstly, we introduce the concepts of $$\varepsilon $$ ε -efficient elements and weakly $$\varepsilon $$ ε -efficient elements of a set with VOSs given by coradiant sets. Secondly we derive characterization theorems for weakly $$\varepsilon $$ ε -efficient solutions in the sense of linear scalarization. Then, we establish characterization theorems for weakly $$\varepsilon $$ ε -efficient solutions in the sense of nonlinear scalarization via the Hirriart-Urruty nonlinear functions and the functions defined via the Kasimbeyli’s augmented dual cones. Finally, we establish nonlinear scalarization theorems for the weakly $$\varepsilon $$ ε -efficient elements of a set via the augmented dual cones approach. The results of this paper generalize the corresponding results in the literature.