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Cutting Plane Algorithms and Approximate Lower Subdifferentiability

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Listed:
  • Jean-Paul Penot

    (Université de Pau)

  • Pham Hong Quang

    (NCSR of Vietnam)

Abstract

A notion of boundedly ε-lower subdifferentiable functions is introduced and investigated. It is shown that a bounded from below, continuous, quasiconvex function is locally boundedly ε-lower subdifferentiable for every ε>0. Some algorithms of cutting plane type are constructed to solve minimization problems with approximately lower subdifferentiable objective and constraints. In those algorithms an approximate minimizer on a compact set is obtained in a finite number of iterations provided some boundedness assumption be satisfied.

Suggested Citation

  • Jean-Paul Penot & Pham Hong Quang, 2011. "Cutting Plane Algorithms and Approximate Lower Subdifferentiability," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 455-470, March.
    • Handle: RePEc:spr:joptap:v:148:y:2011:i:3:d:10.1007_s10957-010-9762-6
    DOI: 10.1007/s10957-010-9762-6
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    References listed on IDEAS

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    1. Jean-Paul Penot & Michel Volle, 1990. "On Quasi-Convex Duality," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 597-625, November.
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