# Introduction to Nonsmooth Analysis and Optimization

arXiv: https://arxiv.org/abs/2001.00216 · HTML: https://mlsanity.com/paper/2001.00216/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jan 2020.

## Built on by (most cited first, 4 of 4)

- [Exact Reformulation and Optimization for Direct Metric Optimization in Binary Imbalanced Classification](https://mlsanity.com/paper/2507.15240/) (2025)
- [Beyond Expectations: Learning with Stochastic Dominance Made Practical](https://mlsanity.com/paper/2402.02698/) (2024)
- [Prediction techniques for dynamic imaging with online primal-dual methods](https://mlsanity.com/paper/2405.02497/) (2024)
- [Proximal methods for point source localisation](https://mlsanity.com/paper/2212.02991/) (2022)

## Abstract (arXiv)

Functions that are not differentiable in the classical sense have become a central tool in modern mathematical models for imaging, inverse problems, machine learning, and optimal control of differential equations. These models are increasingly formulated in infinite-dimensional function spaces to be independent of problem size and discretization quality. This book presents a unified and rigorous introduction to the infinite-dimensional analysis and algorithmic solution of nonsmooth optimization problems arising from the above-mentioned models, from the necessary theoretical tools of nonsmooth analysis to state-of-the-art algorithms and their convergence and stability analysis.