Kính mời quý thầy cô, nghiên cứu sinh, học viên cao học các sinh viên quan tâm sắp xếp thời gian đến tham dự buổi seminar Tối ưu hoá và Ứng dụng do Bộ môn Tối Ưu - Hệ Thống, ĐH Khoa học Tự nhiên TPHCM và Bộ môn Toán, ĐH Quốc tế Hồng Bàng đồng tổ chức, với nội dung sau:
Báo cáo: An Introduction to Set Optimization Problems
Người trình bày: GS.TS. Lâm Quốc Anh (Đại học Cần Thơ)
Thời gian: Chủ nhật - 18.10.2020 - 09h15
Địa điểm: Trường Đại học Quốc tế Hồng Bàng, 215 Điện Biên Phủ, P. 15, Q. Bình Thạnh, Tp. Hồ Chí Minh.
Abstract: In this talk we speak about optimization problems of set-valued mappings on ordered sets. This is a new research direction in optimization, which appeared several decades ago to meet both the theoretical development and practical application demand, and has been extensively investigated so far. The aim of the talk is to provide a comprehensive introduction to the topic, whose content is fourfold.
(a) Firstly, we discuss many ordering relations on the power sets of ordered sets, which play the standards for ordering different sets. On the power sets of preordered sets, we introduce three preordering relations based on the given preorder relations.
(b) Secondly, we consider two criteria of a solution associated with a set-valued optimization problem, a vector criterion and a set criterion, and show some links between their solutions.
(c) Thirdly, we investigate relationships between set optimization problems with some problems related to optimization.
(d) Finally, under suitable conditions, we study many qualitative properties of weak/strong or Pareto efficient solutions of such problems.
Keywords: Set optimization problem, vector optimization problem, set less relation, scalarization method
References
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[3] Gutiérrez, C., Miglierina, E., Molho, E., Novo, V.: Convergence of solutions of a set optimization problem in the image space. J. Optim. Theory Appl. 170(2), 358–371 (2016)
[4] Hamel, A.H., Heyde, F., Löhne, A., Rudloff, B., Schrage, C.: Set optimization and applications-the state of the art. In: Springer Proceedings in Mathematics & Statistics, vol. 151, (2015)
[5] Khan, A.A., Tammer, C., Zălinescu, C.: Set-Valued Optimization. Springer, Berlin (2016)