Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator

2012/12/18 by Jonathan M. Borwein, Borwein, Jonathan M., Liangjin Yao +1
Computer Science · Mathematics · #47H05 #47N10 #90C25 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Optimization and Control (math.OC) #Optimization and Variational Analysis #Primary 47A06 #Secondary 47B65

paper · pdf · doi:10.48550/arxiv.1212.4266

openalex publication_date 2012/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal monotonicity of A+B provided that A, B are maximally monotone and A is a linear relation, as soon as Rockafellar's constraint qualification holds: \dom A∩\inte\dom B≠\varnothing. Moreover, A+B is of type (FPV).

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