# Monotone Operator Theory in Convex Optimization

arXiv: https://arxiv.org/abs/1802.02694 · HTML: https://mlsanity.com/paper/1802.02694/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2018.

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## Abstract (arXiv)

Several aspects of the interplay between monotone operator theory and convex optimization are presented. The crucial role played by monotone operators in the analysis and the numerical solution of convex minimization problems is emphasized. We review the properties of subdifferentials as maximally monotone operators and, in tandem, investigate those of proximity operators as resolvents. In particular, we study new transformations which map proximity operators to proximity operators, and establish connections with self-dual classes of firmly nonexpansive operators. In addition, new insights and developments are proposed on the algorithmic front.