Mathematical Methods of Operations Research

, Volume 48, Issue 2, pp 169–179 | Cite as

A nonconvex separation property in Banach spaces

  • Jonathan M. Borwein
  • Alejandro Jofré


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.

Key words: Subgradients nonconvex separation singular multiplier normal vectors 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jonathan M. Borwein
    • 1
  • Alejandro Jofré
    • 2
  1. 1.CECM, Department of Mathematics and Statistics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada (e-mail:
  2. 2.Departamento de Ingeniería Matemática Universidad de Chile, Casilla 170, correo 3, Santiago, Chile (e-mail:

Personalised recommendations