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. | 107 TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 20, SỐ K2-2017 Approximations of Variational Problems in Terms of Variational Convergence Huynh Thi Hong Diem 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. Index Terms— Variational variational properties saddle points problems multiobjective optimization convergence equilibrium 1 INTRODUCTION V ariational convergence has been considered for half a century with many important applications because it preserves variational properties. This preservation means that, when a sequence of functions converges to a limit function, properties such as being infimum or supremum values, minimizers, maximizes, minsup or maxinf values, minsup-points, saddle points, etc, of these Manuscript Received on July 13th, 2016. Manuscript Revised December 06th, 2016. This research is funded by Ho Chi Minh City University of Technology - VNU-HCM under grant number T-KUD-2017-33 Huynh Thi Hong Diem, Department of Mathematics, Ho Chi Minh City University of Technology, Vietnam National University Hochiminh City, Vietnam. Email: .
