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arXiv · 2001.00216

Introduction to Nonsmooth Analysis and Optimization

Christian Clason·Tuomo Valkonen
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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.

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Christian Clason, Tuomo Valkonen. 2020-01-01. Introduction to Nonsmooth Analysis and Optimization. https://doi.org/10.1137/1.9781611978995

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