Some Remarks on Greenberg–Pierskalla Subdifferentiability of Quasiconvex Functions

We observe that a quasiconvex function which is evenly quasiconvex at a point is not necessarily Greenberg–Pierskalla (briefly, G-P) subdifferentiable at that point, but we prove that a quasiconvex function which is upper semicontinuous on the segments of its effective domain is G-P subdifferentiabl...

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Bibliographic Details
Published in:Vietnam journal of mathematics 2020-06, Vol.48 (2), p.391-406
Main Authors: Volle, M., Martínez-Legaz, J. E.
Format: Article
Language:English
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Mathematics
Mathematics and Statistics
Optimization and Control
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Summary:We observe that a quasiconvex function which is evenly quasiconvex at a point is not necessarily Greenberg–Pierskalla (briefly, G-P) subdifferentiable at that point, but we prove that a quasiconvex function which is upper semicontinuous on the segments of its effective domain is G-P subdifferentiable on the relative interior of this effective domain. We give an application to surrogate duality in quasiconvex programming.
ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-020-00391-6