Introduction to Nonsmooth Analysis and Optimization

Introduction to Nonsmooth Analysis and Optimization offers a thorough examination of analysis and algorithms—first- and second-order methods—in infinite dimensions, as well as a self-contained and accessible introduction to set-valued and variational analysis for optimization problems (including novel calculus results for relevant situations). It is accompanied by Julia code to replicate the numerical results.

This book is intended for advanced undergraduate and graduate students with a solid background in calculus and linear algebra. Prior knowledge of functional analysis and nonlinear optimization is helpful but not assumed. Researchers in data science and machine learning who have an interest in the mathematical foundations of modern nonsmooth optimization algorithms will also find the book useful.

This book is appropriate for courses in convex analysis, nonsmooth optimization, and set-valued/variational analysis.