On Some Generalized Polyhedral Convex Constructions
Người báo cáo: Nguyễn Ngọc Luân

Thời gian: 9h, Thứ 4, ngày 3/5/2017
Địa điểm: Phòng 4, nhà A14, Viện Toán học, 18 Hoàng Quốc Việt, Hà Nội
Tóm tắt: Generalized polyhedral convex sets, generalized polyhedral convex functions on locally convex Hausdorff topological vector spaces, and the related constructions such as sum of sets, sum of functions, directional derivative, infimal convolution, normal cone, conjugate function, subdifferential, are studied thoroughly in this paper. Among other things, we show how a generalized polyhedral convex set can be characterized via the finiteness of the number of its faces. In addition, it is proved that the infimal convolution of a generalized polyhedral convex function and a polyhedral convex function is a polyhedral convex function. The obtained results can be applied to scalar optimization problems described by generalized polyhedral convex sets and generalized polyhedral convex functions.

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