# Conical averagedness and convergence analysis of fixed point algorithms

arXiv: https://arxiv.org/abs/1910.14185 · HTML: https://mlsanity.com/paper/1910.14185/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2019.

## Built on by (most cited first, 2 of 2)

- [Revisiting Inexact Fixed-Point Iterations for Min-Max Problems: Stochasticity and Structured Nonconvexity](https://mlsanity.com/paper/2402.05071/) (2024)
- [Stable Nonconvex-Nonconcave Training via Linear Interpolation](https://mlsanity.com/paper/2310.13459/) (2023)

## Abstract (arXiv)

We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the stability under relaxations, convex combinations and compositions. We derive conical averagedness properties of resolvents of generalized monotone operators. These properties are then utilized in order to analyze the convergence of the proximal point algorithm, the forward-backward algorithm, and the adaptive Douglas-Rachford algorithm. Our study unifies, improves and casts new light on recent studies of these topics.