A study of projectionally exposed cones

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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:	[Graduate Institute & Department of Mathematics] Journal Article

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