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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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  • Hui Hu

    (Northern Illinois University)

  • Qing Wang

    (The World Gates, Inc.)

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.

Suggested Citation

  • Hui Hu & Qing Wang, 2011. "Closedness of a Convex Cone and Application by Means of the End Set of a Convex Set," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 633-645, December.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:3:d:10.1007_s10957-011-9823-5
    DOI: 10.1007/s10957-011-9823-5
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    References listed on IDEAS

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    1. Hui Hu, 2005. "Characterizations of the Strong Basic Constraint Qualifications," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 956-965, November.
    2. A. Moldovan & L. Pellegrini, 2009. "On Regularity for Constrained Extremum Problems. Part 1: Sufficient Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 147-163, July.
    3. A. Moldovan & L. Pellegrini, 2009. "On Regularity for Constrained Extremum Problems. Part 2: Necessary Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 165-183, July.
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    Cited by:

    1. X. Yang & K. Meng, 2014. "Comments on: Farkas’ Lemma: three decades of generalizations for mathematical optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 38-40, April.
    2. Kaiwen Meng & Vera Roshchina & Xiaoqi Yang, 2015. "On Local Coincidence of a Convex Set and its Tangent Cone," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 123-137, January.

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