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A nonconvex separation property in Banach spaces

Author

Listed:
  • Jonathan M. Borwein
  • Alejandro Jofré

Abstract

We establish, in infinite dimensional Banach space, a nonconvex separation property for general closed sets that is an extension of Hahn-Banach separation theorem. We provide some consequences in optimization, in particular the existence of singular multipliers and show the relation of our property with the extremal principle of Mordukhovich. Copyright Springer-Verlag Berlin Heidelberg 1998

Suggested Citation

  • Jonathan M. Borwein & Alejandro Jofré, 1998. "A nonconvex separation property in Banach spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 169-179, November.
    • Handle: RePEc:spr:mathme:v:48:y:1998:i:2:p:169-179
    DOI: 10.1007/s001860050019
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    Cited by:

    1. Hoa T. Bui & Alexander Y. Kruger, 2019. "Extremality, Stationarity and Generalized Separation of Collections of Sets," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 211-264, July.
    2. Flam, S.D. & Jourani, A., 2000. "Prices and Pareto Optima," Norway; Department of Economics, University of Bergen 0800, Department of Economics, University of Bergen.
    3. Alexander Y. Kruger & Marco A. López, 2012. "Stationarity and Regularity of Infinite Collections of Sets," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 339-369, August.
    4. Zdzisław Naniewicz, 2007. "Pseudomonotonicity and Economic Equilibrium Problem in Reflexive Banach Space," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 436-466, May.

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