Nonsmooth Optimization

by Marko M. Makela &. Pekka Neittaanmaki

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Nonsmooth Analysis, Optimization, and Control

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Nonsmooth Analysis, Optimization, and Control

The book builds from nonsmooth differential calculus to optimization methods, then applies those methods to optimal-control problems governed by partial differential equations. Its coverage includes a proximal bundle method for nonsmooth, nonconvex optimization with nonsmooth constraints, alongside practical examples involving process control and optimal shape design. The progression links foundational tools with algorithmic development and applications, making the volume a focused treatment of how nonsmooth methods are formulated and used in control-related problems.

Good fit for readers who enjoy

Readers seeking an elementary, self-contained introduction to nonsmooth analysis and optimization.
Researchers or graduate-level practitioners interested in nonsmooth optimal control and PDE-governed systems.
Readers studying process control or optimal shape design problems.

Themes

Nonsmooth differential calculusNonsmooth optimization methodsOptimal controlPartial differential equationsProcess control and optimal shape design

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Book overview

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.

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