Approximate Solutions for Multi-Objective Optimization Problems via Scalarizing and Nonscalarizing Methods

Ta Quang Son, Hua Khac Bao, Narin Petrot

Full PDF

abstract_carpathian_2026_42_2_457-482

https://doi.org/10.37193/CJM.2026.02.14

Published on 14 February 2026

Issue no: Vol 42/2026 no. 2 Tags: $\varepsilon$-quasi normal set, $\varepsilon$-quasi subdifferential, almost weakly $\epsilon$-Pareto solutions, almost $\epsilon$-Pareto solutions

Description

Abstract.

In this paper, max-ordering and weighted compromising methods are employed to investigate approximate Pareto solutions for a class of multi-objective optimization problems with an infinite number of constraints. Approximate optimality conditions for $\varepsilon$ -quasi Pareto solutions and almost $\varepsilon$ -quasi Pareto solutions of the considered problems are established. The results are derived using a new notion of $\varepsilon$ -quasi subdifferentials for locally Lipschitz functions and $\varepsilon$ -quasi normal sets. Approximate duality theorems are also introduced. In particular, the relationships between the original multi-objective optimization problem and its dual are analyzed via a corresponding pair of primal-dual scalar problems. Several examples are provided to illustrate the proposed notions and to demonstrate the applicability of the obtained results.