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Characterizations of nonsmooth robustly quasiconvex functions. (English) Zbl 1417.49014

The characterization of convexity or generalized convexity in terms of subdifferentials is a central topic in optimization theory and variational analysis, and there are many significant contributions in this way. In this work, the authors follow this line and propose two criteria characterizing the robust quasiconvexity of a lower semicontinuous function in Asplund spaces by using Fréchet subdifferentials.

MSC:

49J52 Nonsmooth analysis
26A48 Monotonic functions, generalizations
26A51 Convexity of real functions in one variable, generalizations
49J53 Set-valued and variational analysis
49J50 Fréchet and Gateaux differentiability in optimization
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