Perspective Functions with Nonlinear Scaling
Functional Analysis
2023-10-18 v2
Abstract
The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivated by applications in several areas of applied analysis, we investigate an extension of this construct in which the scaling variable is replaced by a nonlinear term. Our construction is placed in the general context of locally convex spaces and it generates a lower semicontinuous convex function under broad assumptions on the underlying functions. Various convex-analytical properties are established and closed-form expressions are derived. Several applications are presented.
Cite
@article{arxiv.2210.16937,
title = {Perspective Functions with Nonlinear Scaling},
author = {Luis M. Briceño-Arias and Patrick L. Combettes and Francisco J. Silva},
journal= {arXiv preprint arXiv:2210.16937},
year = {2023}
}