Introduction to Nonsmooth Analysis and Optimization

TL;DR

This book provides a comprehensive introduction to nonsmooth analysis and optimization in infinite-dimensional spaces, covering theoretical foundations and modern algorithms for applications in imaging, machine learning, and control.

Contribution

It offers a unified, rigorous treatment of nonsmooth analysis and algorithms specifically tailored for infinite-dimensional optimization problems in various modern applications.

Findings

Introduces theoretical tools for nonsmooth analysis in infinite-dimensional spaces.

Presents state-of-the-art algorithms with convergence and stability analysis.

Covers applications in imaging, inverse problems, machine learning, and control.

Abstract

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.