Monotone Linear Relations: Maximality and Fitzpatrick Functions
Functional Analysis
2008-05-29 v1 Optimization and Control
Abstract
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.
Cite
@article{arxiv.0805.4256,
title = {Monotone Linear Relations: Maximality and Fitzpatrick Functions},
author = {Heinz H. Bauschke and Xianfu Wang and Liangjin Yao},
journal= {arXiv preprint arXiv:0805.4256},
year = {2008}
}