The sum of a maximally monotone linear relation and the subdifferential of a proper lower semicontinuous convex function is maximally monotone
نویسنده
چکیده
The most important 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 + ∂f provided that A is a maximally monotone linear relation, and f is a proper lower semicontinuous convex function satisfying domA ∩ int dom ∂f ̸= ∅. Moreover, A+ ∂f is of type (FPV). The maximal monotonicity of A+ ∂f when int dom A ∩ dom ∂f ̸= ∅ follows from a result by Verona and Verona, which the present work complements. 2010 Mathematics Subject Classification: Primary 47A06, 47H05; Secondary 47B65, 47N10, 90C25
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