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Regularity Conditions for the Linear Separation of Sets

Author

Listed:
  • G. Bigi

    (University of Pisa)

  • M. Pappalardo

    (University of Pisa)

Abstract

In this paper, we study the linear separation between a set and a convex cone. We introduce the concepts of regularity and total regularity of the separation with respect to a face of the cone and we give theorems characterizing them.

Suggested Citation

  • G. Bigi & M. Pappalardo, 1998. "Regularity Conditions for the Linear Separation of Sets," Journal of Optimization Theory and Applications, Springer, vol. 99(2), pages 533-540, November.
    • Handle: RePEc:spr:joptap:v:99:y:1998:i:2:d:10.1023_a:1021738714110
    DOI: 10.1023/A:1021738714110
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    References listed on IDEAS

    as
    1. M. Castellani & G. Mastroeni & M. Pappalardo, 1997. "Separation of Sets, Lagrange Multipliers, and Totally Regular Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 249-261, February.
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    Cited by:

    1. Shengjie Li & Yangdong Xu & Manxue You & Shengkun Zhu, 2018. "Constrained Extremum Problems and Image Space Analysis–Part I: Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 609-636, June.
    2. M. C. Maciel & S. A. Santos & G. N. Sottosanto, 2009. "Regularity Conditions in Differentiable Vector Optimization Revisited," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 385-398, August.
    3. Regina S. Burachik & M. M. Rizvi, 2012. "On Weak and Strong Kuhn–Tucker Conditions for Smooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 477-491, November.
    4. G. Bigi & M. Pappalardo, 1999. "Regularity Conditions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 83-96, July.

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    1. G. Bigi & M. Pappalardo, 1999. "Regularity Conditions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 83-96, July.
    2. Shengjie Li & Yangdong Xu & Manxue You & Shengkun Zhu, 2018. "Constrained Extremum Problems and Image Space Analysis–Part I: Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 609-636, June.
    3. M. C. Maciel & S. A. Santos & G. N. Sottosanto, 2009. "Regularity Conditions in Differentiable Vector Optimization Revisited," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 385-398, August.

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