Cutting Plane Algorithms and Approximate Lower Subdifferentiability

Jean-Paul Penot () and Pham Hong Quang
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Jean-Paul Penot: Université de Pau
Pham Hong Quang: NCSR of Vietnam

Journal of Optimization Theory and Applications, 2011, vol. 148, issue 3, No 2, 455-470

Abstract: 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.

Keywords: Approximate minimization; Cutting plane method; ε-lower subgradient; Lower subdifferential; Nonsmooth optimization; Quasiconvex function (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10957-010-9762-6

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