Generalized Differential Calculus in Infinite-Dimensional Convex Analysis via Quasi-Relative Interiors
Dang Van Cuong, Boris S. Mordukhovich, Nguyen Mau Nam · arXiv (Cornell University) · 2018
This paper aims at providing further studies of the notion of quasi-relative interior for convex sets introduced by Borwein and Lewis. We obtain new formulas for representing quasi-relative interiors of convex graphs of set-valued mappings and for convex epigraphs of extended-real-valued functions defined on locally convex topological vector spaces. We also show that the role, which this notion plays in infinite dimensions and the results obtained in this vein, are similar to those involving relative interior in finite-dimensional spaces.