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    Title: A study of projectionally exposed cones
    Authors: Sung, Chen-Han;Tam, Bit-Shun
    Contributors: 淡江大學數學學系
    Date: 1990-10
    Issue Date: 2013-06-13 11:25:08 (UTC+8)
    Publisher: Philadelphia: Elsevier Inc.
    Abstract: In view of possible applications to abstract convex programs, Barker, Laidacker, and Poole have made an initial study of p-exposed cones and o.p.-exposed cones by restricting their attention to closed, pointed cones. A study of these cones is continued in this paper. Sufficient conditions for a face of a proper cone to be a p-exposed or an o.p.-exposed face are established. Characterizations of o.p.-exposed cones among polyhedral cones are also obtained. The relation between exposedness and p-exposedness of faces of a general cone is examined. As one consequence, a question posed by Iochum is answered in the finite dimensional case; that is, there is no finite-dimensional semiregular self-dual cones which are not regular. Also, a conjecture posed by Barker and Thompson on p-exposed faces of P(n), that the cone of all real polynomials of degree⩽n which are nonnegative on the closed interval [0,1], is settled.
    Relation: Linear Algebra and Its Applications 139, pp.225-252
    DOI: 10.1016/0024-3795(90)90401-W
    Appears in Collections:[數學學系暨研究所] 期刊論文

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