A general representation of delta-normal sets to sublevels of convex functions
Optimization and Control
2017-10-30 v1 Functional Analysis
Abstract
The (delta-) normal cone to an arbitrary intersection of sublevel sets of proper, lower semicontinuous, and convex functions is characterized, using either epsilon-subdifferentials at the nominal point or exact subdifferentials at nearby points. Our tools include (epsilon-) 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).
Keywords
Cite
@article{arxiv.1710.10187,
title = {A general representation of delta-normal sets to sublevels of convex functions},
author = {Abderrahim Hantoute and Anton Svensson},
journal= {arXiv preprint arXiv:1710.10187},
year = {2017}
}