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

被引：0

作者：

Jian-Wen Peng ^{[1
]}

Wen-Bin Wei ^{[1
]}

Refail Kasimbeyli ^{[2
]}

机构：

[1] School of Mathematical Sciences, Chongqing Normal University, Shapingba, Chongqing

[2] Department of Industrial Engineering, Eskisehir Technical University, Eskisehir

[3] UNEC Mathematical Modeling and Optimization Research Center, Azerbaijan State University of Economics, Baku

来源：

Journal of Optimization Theory and Applications | 2025年 / 206卷 / 1期

基金：

中国国家自然科学基金;

关键词：

Coradiant set; Linear scalarization; Nonlinear scalarization; Variable ordering structure; Vector optimization;

D O I：

10.1007/s10957-025-02662-z

中图分类号：

学科分类号：

摘要：

This paper investigates linear and nonlinear scalarization methods for vector optimization problems with variable ordering structures (VOS). Firstly, we introduce the concepts of ε-efficient elements and weakly ε-efficient elements of a set with VOSs given by coradiant sets. Secondly we derive characterization theorems for weakly ε-efficient solutions in the sense of linear scalarization. Then, we establish characterization theorems for weakly 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 ε-efficient elements of a set via the augmented dual cones approach. The results of this paper generalize the corresponding results in the literature. © The Author(s) 2025.

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