Characterizations of generalized convexities via generalized directional derivatives
Phạm Hữu Sách, Jean‐Paul Penot · Numerical Functional Analysis and Optimization · 1998
The paper gives characterizations of convexity, quasiconvexity, invexity and pseudoconvexity for a (radially) upper-semicontinuous function f in a topological vector space via appropriate properties of a bifunction which is majorized by the upper radial derivative of f and which stands for a generalized derivative of some sort.