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A nonconvex separation property in Banach spaces

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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.

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Authors and Affiliations

  1. CECM, Department of Mathematics and Statistics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada (e-mail: jborwein@cecm.sfu.ca), , , , , , CA

    Jonathan M. Borwein

  2. Departamento de Ingeniería Matemática Universidad de Chile, Casilla 170, correo 3, Santiago, Chile (e-mail: ajofre@dim.uchile.cl), , , , , , CL

    Alejandro Jofré

Authors
  1. Jonathan M. Borwein
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  2. Alejandro Jofré
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Received October 1997/Revised version February 1998

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Borwein, J., Jofré, A. A nonconvex separation property in Banach spaces. Mathematical Methods of OR 48, 169–179 (1998). https://doi.org/10.1007/s001860050019

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  • DOI: https://doi.org/10.1007/s001860050019

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