| We establish a sequential description of the subdifferential sum formula for proper lower semicontinuous convex functions. Motivated by this description, we introduce the notion of an asymptotic sum of two maximal monotone operators, generated by enlargements of the operators, and examine the relationships with the pointwise sum of the maximal monotone operators. We also present various sufficient conditions, including a new dual condition, for the equality of the asymptotic sum and the pointwise sum of two maximal monotone operators
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