Separable reduction and extremal principles in variational analysis. (Q1347444)

From the Introduction: ``This paper is devoted to extremal principles and variational analysis that play an important role in the study of optimization-related problems and their applications. Our main objective is to develop the method of separable reduction for Fréchet-like normals, subgradients, and their \(\varepsilon\)-counterparts in nonseparable Banach spaces that can be applied to extremal principles. Based on these developments, we obtain new direct proofs of two versions of the extremal principle, via Fréchet-like normals and \(\varepsilon\)-normals, respectively, that both provide characterizations of Asplund spaces''.