Geodesic
First Order Characterizations of Pseudoconvex Functions
Serdica Mathematical Journal, Tome 27 (2001) no. 3, pp. 203-218.

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First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed. Well-known first order characterizations of the solution sets of pseudolinear programs are generalized to the case of pseudoconvex programs. The concepts of pseudoconvexity and invexity do not depend on a single definition of the generalized directional derivative.
Keywords: Generalized Convexity, Nonsmooth Function, Generalized Directional Derivative, Pseudoconvex Function, Quasiconvex Function, Invex Function, Nonsmooth Optimization, Solution Sets, Pseudomonotone Generalized Directional Derivative 
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     title = {First {Order} {Characterizations} of {Pseudoconvex} {Functions}},
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Ivanov, Vsevolod. First Order Characterizations of Pseudoconvex Functions. Serdica Mathematical Journal, Tome 27 (2001) no. 3, pp. 203-218. http://geodesic.mathdoc.fr/item/SMJ2_2001_27_3_a1/