Work

Linear and Nonlinear Scalarization Methods for Vector Optimization Problems with Variable Ordering Structures

Year: 2025

Type: article

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.

Source: Journal of Optimization Theory and Applications

DOI: 10.1007/s10957-025-02662-z

Authors: Jian-Wen Peng, Wen-Bin Wei, Refail Kasimbeyli

Institutions: Chongqing Normal University, Azerbaijan State University of Economics, Eskisehir Technical University

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: National Natural Science Foundation of China, Chongqing University, Chongqing Science and Technology Innovation Leading Talent Support Program, Chongqing Basic Science and Advanced Technology Research Program