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Separation Theorem Based on the Quasirelative Interior and Application to Duality Theory

  • F. Cammaroto
  • B. Di Bella
TECHNICAL NOTE

Abstract

We present a separation theorem in which the classic interior is replaced by the quasirelative interior. We apply this result to a constrained problem in the infinite-dimensional convex case, making use of a condition replacing the standard Slater condition, which in some cases can fail.

Keywords

Separation theorems quasirelative interior duality theory 

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References

  1. Borwein, J.M., Lewis, A.S. 1992Partially-Finite Convex Programming, Part 1: Quasisrelative Interiors and Duality Theory.Mathematical Programming571548Google Scholar
  2. Borwein, J. M., and Goebel, R., Notions of Relative Interior in Banach Spaces, Preprint, 2001.Google Scholar
  3. Jahn, J. 1996Introduction to the Theory of Nonlinear OptimizationSpringer VerlagNew York, NYGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • F. Cammaroto
    • 1
  • B. Di Bella
    • 2
  1. 1.Assistant Professor, Department of Mathematics, Faculty of ScienceUniversity of MessinaMessinaItaly
  2. 2.Assistant Professor, Department of Mathematics, Faculty of EngineeringUniversity of MessinaMessinaItaly

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