Description
Book SynopsisThis 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.
Table of ContentsPart 1 Nonsmooth analysis: introduction; convex analysis; nonsmooth differential theory; nonsmooth geometry; nonsmooth optimization theory. Part 2 Nonsmooth optimization: introduction; a survey of bundle methods; proximal bundle method for nonconvex constrained optimization; numerical experiments. Part 3 Nonsmooth optimal control: distributed parameter control problems; optimal shape design; boundary control for Stefan type problems.
