# Nonsmooth Analysis and Optimization

arXiv: https://arxiv.org/abs/1708.04180 · HTML: https://mlsanity.com/paper/1708.04180/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Aug 2017.

## Built on by (most cited first, 5 of 5)

- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [Signal Recovery with Non-Expansive Generative Network Priors](https://mlsanity.com/paper/2204.13599/) (2022)
- [Exact Recovery Guarantees for Parameterized Nonlinear System Identification Problem under Sparse Disturbances or Semi-Oblivious Attacks](https://mlsanity.com/paper/2409.00276/) (2024)
- [Screening for a Reweighted Penalized Conditional Gradient Method](https://mlsanity.com/paper/2107.01106/) (2021)
- [Accelerated Fully First-Order Methods for Bilevel and Minimax Optimization](https://mlsanity.com/paper/2405.00914/) (2024)

## Abstract (arXiv)

These lecture notes for a graduate course cover generalized derivative concepts useful in deriving necessary optimality conditions and numerical algorithms for nondifferentiable optimization problems in inverse problems, imaging, and PDE-constrained optimization. Treated are convex functions and subdifferentials, Fenchel duality, monotone operators and resolvents, Moreau--Yosida regularization, proximal point and (some) first-order splitting methods, Clarke subdifferentials, and semismooth Newton methods. The required background from functional analysis and calculus of variations is also briefly summarized.