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Separation of Sets, Lagrange Multipliers, and Totally Regular Extremum Problems

Author

Listed:
  • M. Castellani

    (University of Pisa)

  • G. Mastroeni

    (University of Pisa)

  • M. Pappalardo

    (University of Pisa)

Abstract

We introduce the concept of total regularity for the separation of sets, and we give a characterization of it. Also, we prove the equivalence between total regularity and boundedness of the generalized multipliers associated to the separation, and we compute the value of the bound. Then, we give a theorem concerning the uniqueness of such multipliers. Afterward, the previous results are applied to the study of the impossibility of generalized systems; particular attention is devoted to systems arising from the optimality conditions of constrained extremum problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:92:y:1997:i:2:d:10.1023_a:1022698811948
    DOI: 10.1023/A:1022698811948
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    Citations

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    Cited by:

    1. 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.
    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.
    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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