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Approximations of Variational Problems in Terms of Variational Convergence

Diem Thi Hong Huynh 1, *
  1. Department of Mathematics, Ho Chi Minh City University of Technology, Vietnam National University Hochiminh City, Vietnam
Correspondence to: Diem Thi Hong Huynh, Department of Mathematics, Ho Chi Minh City University of Technology, Vietnam National University Hochiminh City, Vietnam. Email: Nghiado@sci.edu.vn.
Volume & Issue: Vol. 20 No. K2 (2017) | Page No.: 107-116 | DOI: 10.32508/stdj.v20iK2.456
Published: 2017-06-30

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Copyright The Author(s) 2023. This article is published with open access by Vietnam National University, Ho Chi Minh city, Vietnam. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0) which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited. 

Abstract

We show first the definition of variational convergence of unifunctions and their basic variational properties. In the next section, we extend this variational convergence definition in case the functions which are defined on product two sets (bifunctions or bicomponent functions). We present the definition of variational convergence of bifunctions, icluding epi/hypo convergence, minsuplop convergnece and maxinf-lop convergence, defined on metric spaces. Its variational properties are also considered. In this paper, we concern on the properties of epi/hypo convergence to apply these results on optimization proplems in two last sections. Next we move on to the main results that are approximations of typical and important optimization related problems on metric space in terms of the types of variational convergence are equilibrium problems, and multiobjective optimization. When we applied to the finite dimensional case, some of our results improve known one.

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