Overview

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. Introduction to Nonsmooth Analysis and Optimization presents a unified and rigorous introduction to the infinite-dimensional analysis and algorithmic solution of nonsmooth optimization problems arising from the above-mentioned models, including the necessary theoretical tools of nonsmooth analysis to state-of-the-art algorithms and their convergence and stability analysis. Introduction to Nonsmooth Analysis and Optimization offers a thorough examination of analysis and algorithms—first- and second-order methods— in infinite dimensions, a self-contained and accessible introduction to set-valued and variational analysis for optimization problems and includes novel calculus results for relevant situations. Julia code to replicate the numerical results.

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9781611978995

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Christian Clason is Professor of Mathematical Optimization in the Department of Mathematics and Scientific Computing of the University of Graz. His research areas are nonsmooth and PDE-constrained optimization, inverse problems, and applications to biomedical imaging. Tuomo Valkonen is a Principal Scientist at the MODEMAT Research Center in Mathematical Modeling and Optimization. His research areas cover nonsmooth optimization and analysis, bilevel optimization, inverse problems, and relevant aspects of measures and their geometry.

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