Semismooth Newton methods are a modern class of remarkably powerful
and versatile algorithms for solving constrained optimization
problems with partial differential equations (PDEs), variational
inequalities, and related problems. This book provides a
comprehensive presentation of these methods in function spaces,
striking a balance between thoroughly developed theory and
numerical applications. Although largely self-contained, the book
also covers recent developments in the field, such as
state-constrained problems and offers new material on topics such
as improved mesh independence results. The theory and methods are
applied to a range of practically important problems, including
optimal control of semilinear elliptic differential equations,
obstacle problems, and flow control of instationary Navier-Stokes
fluids. In addition, the author covers adjoint-based derivative
computation and the efficient solution of Newton systems by
multigrid and preconditioned iterative methods.
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