# On the maximal monotonicity of the sum of a maximal monotone linear relation and the subdifferential operator of a sublinear function - Mathematics > Functional Analysis

On the maximal monotonicity of the sum of a maximal monotone linear relation and the subdifferential operator of a sublinear function - Mathematics > Functional Analysis - Download this document for free, or read online. Document in PDF available to download.

Abstract: The most important open problem in Monotone Operator Theory concerns themaximal monotonicity of the sum of two maximal monotone operators provided thatRockafellar-s constraint qualification holds.In this note, we provide a new maximal monotonicity result for the sum of amaximal monotone relation and the subdifferential operator of a proper, lowersemicontinuous, sublinear function. The proof relies on Rockafellar-s formulafor the Fenchel conjugate of the sum as well as some results on the Fitzpatrickfunction.

Author: ** Heinz H. Bauschke, Xianfu Wang, Liangjin Yao**

Source: https://arxiv.org/