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Characterizations of generalized convexities via generalized directional derivatives. (English) Zbl 0916.49015
Convexity, quasiconvexity, invexity and pseudoconvexity are characterized for a real-valued radially upper-semicontinuous function $$f$$ on a topological vector space, in terms of appropriate properties of a bifunction which is majorized by the upper radial derivative of $$f$$, and is so a sort of generalized derivative.

##### MSC:
 49J52 Nonsmooth analysis 26B25 Convexity of real functions of several variables, generalizations 90C48 Programming in abstract spaces 90C26 Nonconvex programming, global optimization
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##### References:
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