Some remarks about strictly pseudoconvex functions with respect to the Clarke--Rockafellar subdifferential
Lobachevskii journal of mathematics, Tome 24 (2006), pp. 55-62.

Voir la notice de l'article provenant de la source Math-Net.Ru

Using the notion of radially Clarke–Rockafellar subdifferentiable functions (RCRS-functions), we characterize strictly pseudoconvex functions with respect to the Clarke–Rockafellar subdifferential in two different ways, and we study a maximization problem involving RCRS-strictly pseudoconvex functions over a convex set.
Keywords: strictly pseudoconvex functions, RCRS-functions, strongly RCRS-functions.
@article{LJM_2006_24_a3,
     author = {S. Lahrech and A. Jaddar and A. Ouahab and A. Mbarki},
     title = {Some remarks about strictly pseudoconvex functions with respect to the {Clarke--Rockafellar} subdifferential},
     journal = {Lobachevskii journal of mathematics},
     pages = {55--62},
     publisher = {mathdoc},
     volume = {24},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2006_24_a3/}
}
TY  - JOUR
AU  - S. Lahrech
AU  - A. Jaddar
AU  - A. Ouahab
AU  - A. Mbarki
TI  - Some remarks about strictly pseudoconvex functions with respect to the Clarke--Rockafellar subdifferential
JO  - Lobachevskii journal of mathematics
PY  - 2006
SP  - 55
EP  - 62
VL  - 24
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2006_24_a3/
LA  - en
ID  - LJM_2006_24_a3
ER  - 
%0 Journal Article
%A S. Lahrech
%A A. Jaddar
%A A. Ouahab
%A A. Mbarki
%T Some remarks about strictly pseudoconvex functions with respect to the Clarke--Rockafellar subdifferential
%J Lobachevskii journal of mathematics
%D 2006
%P 55-62
%V 24
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2006_24_a3/
%G en
%F LJM_2006_24_a3
S. Lahrech; A. Jaddar; A. Ouahab; A. Mbarki. Some remarks about strictly pseudoconvex functions with respect to the Clarke--Rockafellar subdifferential. Lobachevskii journal of mathematics, Tome 24 (2006), pp. 55-62. http://geodesic.mathdoc.fr/item/LJM_2006_24_a3/

[1] D. Aussel, Théorème de la valeur moyenne et convexité géneralisée en analyse non régulière, Ph-D Thesis, Université Blaise Pascal, 1994

[2] D. Aussel, “Subdifferential properties of quasiconvex and pseudoconvex functions: unified approach”, J. Optim. Theory Appl., 97:1 (1998), 29–45 | DOI | MR | Zbl

[3] F. H. Clarke, Yu. S. Ledyaev, R. J. Stern and P. R. Wolenski, Nonsmooth analysis and control theory, Springer-Verlag, New York, 1998 | MR

[4] A. Daniilidis and N. Hadjisavvas, On subdifferentials of quasiconvex and pseudoconvex functions and cyclic monotonicity, Les presses de L'Université de Aegean, Greece, 1997

[5] W. E. Diewert, Alternative characterizations of six kinds of quasiconvexity in the nondifferentiable case with applications nonsmooth programming, Academic Press, 1981

[6] A. Hassouni and A. Jaddar, “Quasi-convex functions and applications to optimality conditions in nonlinear programming”, Appl. Math. Lett., 14:2 (2001), 241–244 | DOI | MR | Zbl

[7] A. Hassouni and A. Jaddar, “Sur les fonctions pseudoconvexes et applications l'optimisation globale” (to appear)

[8] J.-B. Hiriart Urruty and Yu. S. Ledyaev, “A note on characterization of the global maxima of a (tangentially) convex functions over a convex set”, J. Convex Anal., 3:1 (1996), 55–31 | MR

[9] O. L. Mangazarian, “Pseudoconvex functions”, SIAM J. Control, 3 (1965), 281–290 | DOI

[10] J.-P. Penot, “Generalized convex functions in the light of non smooth analysis”, Lecture notes in Economics and Math. Systems, 429, Springer Verlag, 1995, 269–291 | MR

[11] J.-P. Penot, “Are generalized derivatives useful for generalized convex functions”, Proceeding of fifth symposium on generalized convexity, 1996, 3–59 | MR