https://repositorio.uoh.cl/handle/611/990 2026-04-07T20:10:07Z https://repositorio.uoh.cl/handle/611/946 TOWARDS SUPREMUM-SUM SUBDIFFERENTIAL CALCULUS FREE OF QUALIFICATION CONDITIONS Correa, R; Hantoute, A; López, MA We give a formula for the subdifferential of the sum of two convex functions where one of them is the supremum of an arbitrary family of convex functions. This is carried out under a weak assumption expressing a natural relationship between the lower semicontinuous envelopes of the data functions in the domain of the sum function. We also provide a new rule for the subdifferential of the sum of two convex functions, which uses a strategy of augmenting the involved functions. The main feature of our analysis is that no continuity-type condition is required. Our approach allows us to unify, recover, and extend different results in the recent literature. 2016-01-01T00:00:00Z