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Monotone linear relations: maximality and Fitzpatrick functions

By Heinz H. Bauschke, Xianfu Wang and Liangjin Yao


Dedicated to Stephen Simons on the occasion of his 70 th birthday 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. 2000 Mathematics Subject Classification

Topics: Adjoint process, Fenchel conjugate, Fitzpatrick family, Fitzpatrick function, linear relation, maximal monotone operator, monotone operator, skew linear relation
Year: 2009
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