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

Jian-Wen Peng (), Wen-Bin Wei () and Refail Kasimbeyli ()
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Jian-Wen Peng: Chongqing Normal University
Wen-Bin Wei: Chongqing Normal University
Refail Kasimbeyli: Eskisehir Technical University

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 1, No 2, 21 pages

Abstract: 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.

Keywords: Vector optimization; Coradiant set; Variable ordering structure; Linear scalarization; Nonlinear scalarization; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02662-z

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