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

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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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115, USA

    Hui Hu

  2. The World Gates, Inc., 11545 Parkwoods Circle, Suite B-1, Alpharetta, GA, 30005, USA

    Qing Wang

Authors
  1. Hui Hu
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  2. Qing Wang
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Correspondence to Hui Hu.

Additional information

Communicated by C. Zălinescu.

The authors wish to thank the referees for their comments and suggestions.

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Hu, H., Wang, Q. Closedness of a Convex Cone and Application by Means of the End Set of a Convex Set. J Optim Theory Appl 151, 633–645 (2011). https://doi.org/10.1007/s10957-011-9823-5

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  • DOI: https://doi.org/10.1007/s10957-011-9823-5

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