Taiwanese Journal of Mathematics

An Approach to $\epsilon$-duality Theorems for Nonconvex Semi-infinite Multiobjective Optimization Problems

Do Sang Kim and Ta Quang Son

Full-text: Open access

Abstract

Using a scheme for solving multiobjective optimization problems via a system of corresponding scalar problems, approximate optimality conditions for a nonconvex semi-infinite multiobjective optimization problem are established. As a new approach, the scheme is developed to study the approximate duality theorems of the problem via a pair of primal-dual scalar problems. Several $\epsilon$-duality theorems are given. Furthermore, the existence theorem for almost quasi weakly $\epsilon$-Pareto solutions of the primal problem, and the existence theorem for quasi weakly $\epsilon$-Pareto solutions of the dual problem are established without any constraint qualification.

Article information

Source
Taiwanese J. Math., Volume 22, Number 5 (2018), 1261-1287.

Dates
Received: 29 November 2017
Revised: 23 May 2018
Accepted: 3 June 2018
First available in Project Euclid: 12 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1531382431

Digital Object Identifier
doi:10.11650/tjm/180603

Mathematical Reviews number (MathSciNet)
MR3859375

Zentralblatt MATH identifier
06965418

Subjects
Primary: 90C26: Nonconvex programming, global optimization 49N15: Duality theory 90C46: Optimality conditions, duality [See also 49N15]

Keywords
generalized KKT condition up to $\epsilon$ almost quasi $\epsilon$-Pareto solution almost quasi weakly $\epsilon$-Pareto solution Wolfe duality

Citation

Kim, Do Sang; Son, Ta Quang. An Approach to $\epsilon$-duality Theorems for Nonconvex Semi-infinite Multiobjective Optimization Problems. Taiwanese J. Math. 22 (2018), no. 5, 1261--1287. doi:10.11650/tjm/180603. https://projecteuclid.org/euclid.twjm/1531382431


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