# Applications of Convex Analysis within Mathematics

arXiv: https://arxiv.org/abs/1302.1978 · HTML: https://mlsanity.com/paper/1302.1978/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2013.

## Built on by (most cited first, 1 of 1)

- [Distributionally Time-Varying Online Stochastic Optimization under Polyak-Lojasiewicz Condition with Application in Conditional Value-at-Risk Statistical Learning](https://mlsanity.com/paper/2309.09411/) (2023)

## Abstract (arXiv)

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.