  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 $A+\partial f$ provided
that $A$ is a maximally monotone linear relation, and $f$ is a proper lower
semicontinuous convex function satisfying $\dom A\cap\inte\dom \partial
f\neq\varnothing$. Moreover, $A+\partial f$ is of type (FPV). The maximal
monotonicity of $A+\partial f$ when $\intdom A\cap\dom \partial
f\neq\varnothing$ follows from a result by Verona and Verona, which the present
work complements.
