The sum of a maximal monotone operator of type (FPV) and a maximal monotone operator with full domain is maximal monotone

2010/05/13 by Yao, Liangjin
#52A41 #90C25 #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Primary 47H05 #Secondary 49N15

paper · doi:10.48550/arxiv.1005.2247

Abstract

The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximal monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal monotonicity of A+B provided that A and B are maximal monotone operators such that \dom A∩\inte\dom B≠\varnothing, A+N_\dom B is of type (FPV), and \dom A∩\dom B⊆\dom B. The proof utilizes the Fitzpatrick function in an essential way.

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