  We introduce and study a new dual condition which characterizes zero duality
gap in nonsmooth convex optimization. We prove that our condition is weaker
than all existing constraint qualifications, including the closed epigraph
condition. Our dual condition was inspired by, and is weaker than, the
so-called Bertsekas' condition for monotropic programming problems. We give
several corollaries of our result and special cases as applications. We pay
special attention to the polyhedral and sublinear cases, and their implications
in convex optimization.
