Characterizations of Nonsmooth Robustly Quasiconvex Functions

Hoa T. Bui (), Pham Duy Khanh () and Thi Tu Trinh Tran ()
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Hoa T. Bui: Federation University Australia
Pham Duy Khanh: HCMC University of Education
Thi Tu Trinh Tran: Oakland University Michigan

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 3, No 5, 775-786

Abstract: Abstract 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.

Keywords: Quasiconvexity; Robust quasiconvexity; Quasimonotone; Fréchet subdifferential; Approximate mean value theorem; 26A48; 26A51; 49J52; 49J53 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-018-1421-3

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