Properties of generalized nonlinear Gerstewitz scalarization functions and applications

Nguyen Thai Anh , Tran Ngoc Tam * , Tran Thi Bich Tram and Pham Thi Vui

* Corresponding author (tntam@ctu.edu.vn)

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Received: 18 Oct 2025
Revised: 01 Nov 2025
Accepted: 15 Jul 2026
Published: 25 Aug 2026
Title: Properties of generalized nonlinear Gerstewitz scalarization functions and applications
DOI: 10.22144/ctujos.2026.153
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How to Cite
Anh, N. T., Tâm, T. N., Trâm, T. T. B., & Vui, P. T. (2026). Properties of generalized nonlinear Gerstewitz scalarization functions and applications. CTU Journal of Science, 62(4), 113-120. https://doi.org/10.22144/ctujos.2026.153
Issue
Vol. 62 No. 4 (2026)
Section
Natural Sciences

Abstract

Several properties of the generalized nonlinear scalarization function of the Gerstewitz type are investigated. These properties are then employed to study the characteristics of set relations via variable domination structures and Ekeland’s variational principle for vector optimization problems with variable domination structures.

Keywords: Vector optimization problem, variable domination structure, Ekeland variational principle, nonlinear scalarization function

Tóm tắt

Một số tính chất của hàm vô hướng hóa phi tuyến tổng quát dạng Gerstewitz được nghiên cứu. Sau đó, các tính chất này được sử dụng để nghiên cứu các đặc trưng của các quan hệ tập thông qua cấu trúc trội chứa biến và nguyên lý biến phân Ekeland cho bài toán tối ưu véc-tơ với cấu trúc trội chứa biến. 

Từ khóa: Bài toán tối ưu véc-tơ, cấu trúc trội chứa biến, nguyên lý biến phân Ekeland, hàm vô hướng hóa phi tuyến

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