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October, 2018 An Approach to $\epsilon$-duality Theorems for Nonconvex Semi-infinite Multiobjective Optimization Problems
Do Sang Kim, Ta Quang Son
Taiwanese J. Math. 22(5): 1261-1287 (October, 2018). DOI: 10.11650/tjm/180603


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.


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Do Sang Kim. Ta Quang Son. "An Approach to $\epsilon$-duality Theorems for Nonconvex Semi-infinite Multiobjective Optimization Problems." Taiwanese J. Math. 22 (5) 1261 - 1287, October, 2018.


Received: 29 November 2017; Revised: 23 May 2018; Accepted: 3 June 2018; Published: October, 2018
First available in Project Euclid: 12 July 2018

zbMATH: 06965418
MathSciNet: MR3859375
Digital Object Identifier: 10.11650/tjm/180603

Primary: 49N15 , 90C26 , 90C46

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

Rights: Copyright © 2018 The Mathematical Society of the Republic of China


Vol.22 • No. 5 • October, 2018
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