Cutting Plane Algorithms and Approximate Lower Subdifferentiability |
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Authors: | Jean-Paul Penot Pham Hong Quang |
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Institution: | (3) School Inform. Techn. and Math. Sci., University Ballarat, Ballarat, Australia; |
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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. |
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