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On Local Coincidence of a Convex Set and its Tangent Cone

Author

Listed:
  • Kaiwen Meng

    (Southwest Jiaotong University)

  • Vera Roshchina

    (Federation University Australia)

  • Xiaoqi Yang

    (The Hong Kong Polytechnic University)

Abstract

In this paper, we introduce the exact tangent approximation property for a convex set and provide its characterizations, including the nonzero extent of a convex set. We obtain necessary and sufficient conditions for the closedness of the positive hull of a convex set via a limit set defined by truncated upper level sets of the gauge function. We also apply the exact tangent approximation property to study the existence of a global error bound for a proper, lower semicontinuous and positively homogeneous function.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:1:d:10.1007_s10957-014-0582-y
    DOI: 10.1007/s10957-014-0582-y
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    References listed on IDEAS

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    1. 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.
    2. Hui Hu, 2005. "Characterizations of the Strong Basic Constraint Qualifications," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 956-965, November.
    3. Edward J. Anderson & Miguel A. Goberna & Marco A. López, 2001. "Simplex-Like Trajectories on Quasi-Polyhedral Sets," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 147-162, February.
    4. 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. 150(1), pages 52-64, July.
    Full references (including those not matched with items on IDEAS)

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