Applications of Convex Analysis within Mathematics
Functional Analysis
2013-07-23 v2 Optimization and Control
Abstract
In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal convolution in Monotone Operator Theory. Among other things, we recapture the Minty surjectivity theorem in Hilbert space, and present a new proof of the sum theorem in reflexive spaces. More technically, we also discuss autoconjugate representers for maximally monotone operators. Finally, we consider various other applications in mathematical analysis.
Cite
@article{arxiv.1302.1978,
title = {Applications of Convex Analysis within Mathematics},
author = {Francisco J. Aragón Artacho and Jonathan M. Borwein and Victoria Martín-Márquez and Liangjin Yao},
journal= {arXiv preprint arXiv:1302.1978},
year = {2013}
}
Comments
38 pages, minor revision incorporating referees' comments