Subdifferential characterization of quasiconvexity and convexity
Aussel, Didier ; Corvellec, Jean-Noël ; Lassonde, Marc
HAL, hal-00699221 / Harvested from HAL
Text on HAL
Let f : X → R ∪ {+∞} be a lower semicontinuous function on a Banach space X. We show that f is quasiconvex if and only if its Clarke subdifferential ∂f is quasimonotone. As an immediate consequence, we get that f is convex if and only if ∂f is monotone.
Publié le : 1994-07-05
Classification:  [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] 
@article{hal-00699221,
     author = {Aussel, Didier and Corvellec, Jean-No\"el and Lassonde, Marc},
     title = {Subdifferential characterization of quasiconvexity and convexity},
     journal = {HAL},
     volume = {1994},
     number = {0},
     year = {1994},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00699221}
}

Aussel, Didier; Corvellec, Jean-Noël; Lassonde, Marc. Subdifferential characterization of quasiconvexity and convexity. HAL, Tome 1994 (1994) no. 0, . http://gdmltest.u-ga.fr/item/hal-00699221/