Marko M. Mäkelä

This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily di?erentiable optimization). Solving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the context of image denoising, optimal control, neural network training, data mining, economics and computational chemistry and physics. The book covers both the theory and the numerical methods used in NSO and provide an overview of di?erent problems arising in the ?eld. It is organized into three parts:1. convex and nonconvex analysis and the theory of NSO;2. test problems and practical applications;3. a guide to NSO software. The book is ideal for anyone teaching or attending NSO courses. As an accessible introduction to the ?eld, it is also well suited as an independent learning guide for practitioners already familiar with the basics of optimization.

This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily di?erentiable optimization). Solving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the context of image denoising, optimal control, neural network training, data mining, economics and computational chemistry and physics. The book covers both the theory and the numerical methods used in NSO and provide an overview of di?erent problems arising in the ?eld. It is organized into three parts:1. convex and nonconvex analysis and the theory of NSO;2. test problems and practical applications;3. a guide to NSO software. The book is ideal for anyone teaching or attending NSO courses. As an accessible introduction to the ?eld, it is also well suited as an independent learning guide for practitioners already familiar with the basics of optimization.

This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from optimal control of systems covered by partial differential equations. Several practical problems, like process control and optimal shape design problems are considered.