Introduction to Nonsmooth Analysis and Optimization

Explore a rigorous framework for tackling challenges without classical differentiability in imaging, inverse problems, machine learning, and optimal control. Emphasizing infinite-dimensional analysis with advanced nonsmooth calculus tools, it unifies first- and second-order methods, novel results, and practical Julia code.
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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