Characterizations of Nonsmooth Robustly Quasiconvex Functions
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Bui, H.T. and Khanh, P.D. and Tran, T.T.T. 2019. Characterizations of Nonsmooth Robustly Quasiconvex Functions. Journal of Optimization Theory and Applications. 180 (3): pp. 775-786.
Journal of Optimization Theory and Applications
Faculty of Science and Engineering
School of Electrical Engineering, Computing and Mathematical Sciences (EECMS)
This is a post-peer-review, pre-copyedit version of an article published in Characterizations of Nonsmooth Robustly Quasiconvex Functions. The final authenticated version is available online at: http://doi.org/10.1007/s10957-018-1421-3
© 2018, Springer Science+Business Media, LLC, part of Springer Nature. Two criteria for the robust quasiconvexity of lower semicontinuous functions are established in terms of Fréchet subdifferentials in Asplund spaces. The first criterion extends to such spaces a result established by Barron et al. (Discrete Contin Dyn Syst Ser B 17:1693–1706, 2012). The second criterion is totally new even if it is applied to lower semicontinuous functions on finite-dimensional spaces.