A General Representation of δ-normal Sets to Sublevels of Convex Functions

Abstract

The (δ-) normal cone to an arbitrary intersection of sublevel sets of proper, lower semicontinuous, and convex functions is characterized, using either e-subdifferentials at the nominal point or exact subdifferentials at nearby points. Our tools include (e-) calculus rules for sup/max functions. The framework of this work is that of a locally convex space, however, formulas using exact subdifferentials require some restriction either on the space (e.g. Banach), or on the function (e.g. epi-pointed).