National Science Foundation grant #1411817.
Set-Valued and Variational Analysis
Convex geometry, Banach spaces, Mathematical optimization, Convex functions
This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus, we present an overview of some known achievements with their uniﬁed and simpliﬁed proofs based on the developed geometric variational schemes. Key words. Convex and variational analysis, Fenchel conjugates, normals and subgradients, coderivatives, convex calculus, optimal value functions.
Mordukhovich, B. S., Nam, N. M., Rector, R. B., & Tran, T. (2017). Variational geometric approach to generalized differential and conjugate calculi in convex analysis. Set-Valued and Variational Analysis, 25(4), 731-755.