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

Author

Listed:
  • Jian-Wen Peng

    (Chongqing Normal University)

  • Wen-Bin Wei

    (Chongqing Normal University)

  • Refail Kasimbeyli

    (Eskisehir Technical University
    Azerbaijan State University of Economics)

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.

Suggested Citation

  • Jian-Wen Peng & Wen-Bin Wei & Refail Kasimbeyli, 2025. "Linear and Nonlinear Scalarization Methods for Vector Optimization Problems with Variable Ordering Structures," Journal of Optimization Theory and Applications, Springer, vol. 206(1), pages 1-21, July.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:1:d:10.1007_s10957-025-02662-z
    DOI: 10.1007/s10957-025-02662-z
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