Let be a reflexive Banach space and let be a lower semicontinuous convex function which is Gâteaux differentiable on . Assume further that is both locally bounded and single-valued on its domain and is locally bounded on its domain, is strictly convex on every convex subset of . The Bregman distance associated with is the function defined by if and as otherwise. Let , and where is a countable family of closed and convex subsets of .
In this paper the authors present a method for finding the best Bregman approximation to from . A renorming result that the authors attribute to Professor J. D. Vanderwerff, saying that any reflexive space can be equivalently renormed so that in the new norm the space is strictly convex, Gâteaux smooth but fails to have the Kadec-Klee property will also be of interest to a general reader.