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Quasiconvex Minimization on a Locally Finite Union of Convex Sets

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Abstract

Extending the approach initiated in Aussel and Hadjisavvas (SIAM J. Optim. 16:358–367, 2005) and Aussel and Ye (Optimization 55:433–457, 2006), we obtain the existence of a local minimizer of a quasiconvex function on the locally finite union of closed convex subsets of a Banach space. We apply the existence result to some difficult nonconvex optimization problems such as the disjunctive programming problem and the bilevel programming problem.

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Authors and Affiliations

  1. Département de Mathématiques, Université de Perpignan, Perpignan, France

    D. Aussel

  2. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada

    J. J. Ye

Authors
  1. D. Aussel
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  2. J. J. Ye
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Corresponding author

Correspondence to D. Aussel.

Additional information

Communicated by T. Rapcsak.

Dedicated to Jean-Pierre Crouzeix on the occasion of his 65th birthday.

The authors thank two anonymous referees for careful reading of the paper and helpful suggestions. The research of the second author was partially supported by NSERC/Canada.

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Aussel, D., Ye, J.J. Quasiconvex Minimization on a Locally Finite Union of Convex Sets. J Optim Theory Appl 139, 1–16 (2008). https://doi.org/10.1007/s10957-008-9431-1

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  • DOI: https://doi.org/10.1007/s10957-008-9431-1

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