Characterizations of Nonsmooth Robustly Quasiconvex Functions

Two criteria for the robust quasiconvexity of lower semicontinuous functions are established in terms of Frechet 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.