Volume 57, Number 2, March-April 2023
|697 - 714
|28 April 2023
Identifying approximate proper efficiency in an infinite dimensional space
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
* Corresponding author: Ghaznavi@shahroodut.ac.ir
Accepted: 16 February 2023
The main idea of this article is to characterize approximate proper efficiency that is a widely used optimality concept in multicriteria optimization problems that prevents solutions having unbounded trade-offs. We analyze a modification of approximate proper efficiency for problems with infinitely many objective functions. We obtain some necessary and sufficient optimality conditions for this modification of approximate proper efficiency. This modified version of approximation guarantees the general characterizations of approximate properly efficient points as solutions to weighted sum problems and modified weighted Tchebycheff norm problems, even if there is an infinite number of criteria. The provided proofs concerning the modified definition show that if the number of the objective functions is infinite, then these results become invalid under the primary definition of approximate proper efficiency.
Mathematics Subject Classification: Primary 90C29 / Secondary 90C30 / 49M37
Key words: Multiobjective optimization / Approximate proper efficiency / Scalarization technique / Infinitely many criteria
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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