Geodesic
Pseudomonotone Diagonal Subdifferential Operators
Journal of convex analysis, Tome 20 (2013) no. 1, pp. 1-12

Voir la notice de l'article provenant de la source Heldermann Verlag

Let $f$ be an equilibrium bifunction defined on the product space $X\times X$, where $X$ is a Banach space. If $f$ is locally Lipschitz with respect to the second variable, for every $x\in X$ we define $T_f(x)$ as the Clarke subdifferential of $f(x,\cdot)$ evaluated at $x$. This multivalued operator plays a fundamental role for the reformulation of equilibrium problems as variational inequality ones. We analyze additional conditions on $f$ which ensure the $D$-maximal pseudomonotonicity and the cyclically pseudomonotonicity of $T_f$. Such results have consequences in terms of the characterization of the set of solutions of a subclass of pseudomonotone equilibrium problems.
Classification : 91B50, 47H05
Mots-clés : Equilibrium problem, pseudomonotone bifunction, pseudomonotone operator, diagonal subdifferential 
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     author = {M. Castellani and M. Giuli},
     title = {Pseudomonotone {Diagonal} {Subdifferential} {Operators}},
     journal = {Journal of convex analysis},
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     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a0/}
}
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M. Castellani; M. Giuli. Pseudomonotone Diagonal Subdifferential Operators. Journal of convex analysis, Tome 20 (2013) no. 1, pp. 1-12. http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a0/