This book addresses an important class of problems in the field of mathematical optimization – those involving nonconvex and/or nonsmooth continuous functions. The authors introduce the theoretical foundations of nonconvex nonsmooth functions and discuss optimality conditions for optimization problems involving such functions. They also provide a wide-ranging review of the foundations underlying the most effective and efficient algorithms for solving nonconvex nonsmooth optimization problems. This challenging class of problems has applications in areas such as control systems, signal processing, and data science. In Practical Nonconvex Nonsmooth Optimization the authorsdefine problems over finite-dimensional real-vector spaces, so readers do not need an extensive background in functional analysis,use nonconvex smooth optimization as a starting point rather than convex optimization, making it easier for those who do not have an extensive background in convex analysis and optimization, and employ a conversational style and put long technical proofs at the end of each chapter so that the main ideas are understood before looking into the details of long, technical proofs.
