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 Lý thuyết Tối ưu với nội dung sau:
Báo cáo 1: Optimality conditions and duality for nonsmooth semi-infinite programming via convexificators
Người trình bày: TS. Lê Thanh Tùng (ĐH Cần Thơ)
Thời gian: Thứ bảy - 29.10.2016 - 14h00
Địa điểm: phòng B.37 - ĐH Khoa học Tự nhiên, 227 Nguyễn Văn Cừ, Quận 5, TpHCM
Tóm tắt báo cáo: In this paper, we consider nonsmooth semi-infinite programming (SIP) with a feasible set defined by inequality constraints. Necessary and sufficient optimality conditions for local solutions are established in terms of convexificators. Then, we propose types of Wolfe and Mond-Weir dual problems for (SIP) and explore weak and strong duality relations under generalized convexity. Our results can be applied for the non-Lipschitz maps. Some examples
are provided to show advantages of our results.
Báo cáo 2: The boundedness of second-order Karush-Kuhn-Tucker multiplier sets
Người trình bày: TS. Nguyễn Minh Tùng (ĐH Khoa học Tự nhiên TpHCM)
Thời gian: Chủ nhật - 30.10.2016 - 08h30
Địa điểm: phòng F.303 - ĐH Khoa học Tự nhiên, 227 Nguyễn Văn Cừ, Quận 5, TpHCM
Tóm tắt báo cáo: We propose a generalized second-order asymptotic contingent epiderivative of a set-valued mapping, study its properties, relations to some second-order contingent epiderivatives, and sufficient conditions for its existence. Then, using these epiderivatives, we investigate set-valued optimization problems with generalized inequality constraints. Both second-order necessary conditions and sufficient conditions for optimality of the Karush-Kuhn-Tucker type are established under the second-order Kurcyusz-Robinson-Zowe constraint qualification. We also show that this second-order constraint qualification is necessary and suffiient for the boundedness of second-order Karush-Kuhn-Tucker multiplier set. Furthermore,this boundedness is shown to be a sufficient condition for the second-order Kurcyusz-Robinson-Zowe constraint qualification and a relaxed second-order Mangasarian-Fromovitz constraint qualification to be equivalent. The obtained results are new or improve recent existing ones in the literature.