Geodesic
Monotone Linear Relations: Maximality and Fitzpatrick Functions
Journal of convex analysis, Tome 16 (2009) no. 3, pp. 673-686

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

We analyze and characterize maximal monotonicity of linear relations (set-valued operators with linear graphs). An important tool in our study are Fitzpatrick functions. The results obtained partially extend work on linear and at most single-valued operators by Phelps and Simons and by Bauschke, Borwein and Wang. Furthermore, a description of skew linear relations in terms of the Fitzpatrick family is obtained. We also answer one of Simons' problems by showing that if a maximal monotone operator has a convex graph, then this graph must actually be affine.
Classification : 47A06, 47H05, 26B25, 47A05, 49N15, 52A41, 90C25
Mots-clés : Adjoint process, Fenchel conjugate, Fitzpatrick family, Fitzpatrick function, linear relation, maximal monotone operator, monotone operator, skew linear relation 
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     author = {H. H. Bauschke and X. Wang and L. Yao},
     title = {Monotone {Linear} {Relations:} {Maximality} and {Fitzpatrick} {Functions}},
     journal = {Journal of convex analysis},
     pages = {673--686},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_3_JCA_2009_16_3_a4/}
}
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H. H. Bauschke; X. Wang; L. Yao. Monotone Linear Relations: Maximality and Fitzpatrick Functions. Journal of convex analysis, Tome 16 (2009) no. 3, pp. 673-686. http://geodesic.mathdoc.fr/item/JCA_2009_16_3_JCA_2009_16_3_a4/