Closedness of a Convex Cone and Application by Means of the End Set of a Convex Set

Hui Hu () and Qing Wang ()
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Hui Hu: Northern Illinois University
Qing Wang: The World Gates, Inc.

Journal of Optimization Theory and Applications, 2011, vol. 150, issue 1, No 4, 52-64

Abstract: Abstract This article presents new conditions that ensure the closedness of a convex cone in terms of the end set and the extent of its generator. The results significantly extend the classic condition. The new closedness conditions are utilized to obtain a simple formula of the least global error bound and a suitable regularity condition of the set containment problem for sublinear functions.

Keywords: Convex set; Convex cone; The end set of a convex set; The extent of a convex set; Convex function; Sublinear function (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-011-9809-3

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