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

Peng J., Wei W., Kasimbeyli R.

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, vol.206, no.1, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Nəşrin Növü: Article / Article
  • Cild: 206 Say: 1
  • Nəşr tarixi: 2025
  • Doi nömrəsi: 10.1007/s10957-025-02662-z
  • jurnalın adı: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Açar sözlər: Vector optimization, Coradiant set, Variable ordering structure, Linear scalarization, Nonlinear scalarization
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

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.