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Characterizations of Nonsmooth Robustly Quasiconvex Functions

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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.

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology (NAFOSTED) under Grant 101.01–2017.325, and by Vietnam Institute for Advanced Study in Mathematics (VIASM). Hoa T. Bui is supported by an Australian Government Research Training Program (RTP) Stipend and RTP Fee-Offset Scholarship through Federation University Australia. Pham Duy Khanh is supported by FONDECYT postdoc Grant No. 3180080, and by Basal Program CMM–AFB 170001 from CONICYT–Chile. The authors are grateful to the anonymous referees for their careful reading, encouragement, and valuable suggestions.

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Authors and Affiliations

  1. Centre for Informatics and Applied Optimisation, Federation University Australia, Ballarat, VIC, Australia

    Hoa T. Bui

  2. Department of Mathematics, HCMC University of Education, Ho Chi Minh, Vietnam

    Pham Duy Khanh

  3. Center for Mathematical Modeling, Universidad de Chile, Santiago, Chile

    Pham Duy Khanh

  4. Department of Mathematics and Statistics, Oakland University Michigan, Rochester, MI, 48309, USA

    Thi Tu Trinh Tran

Authors
  1. Hoa T. Bui
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  2. Pham Duy Khanh
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  3. Thi Tu Trinh Tran
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Correspondence to Pham Duy Khanh.

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Communicated by Lionel Thibault.

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Bui, H.T., Khanh, P.D. & Tran, T.T.T. Characterizations of Nonsmooth Robustly Quasiconvex Functions. J Optim Theory Appl 180, 775–786 (2019). https://doi.org/10.1007/s10957-018-1421-3

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  • DOI: https://doi.org/10.1007/s10957-018-1421-3

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