  This book aims to give an introduction to generalized derivative concepts
useful in deriving necessary optimality conditions and numerical algorithms for
infinite-dimensional nondifferentiable optimization problems that arise in
inverse problems, imaging, and PDE-constrained optimization. They cover convex
subdifferentials, Fenchel duality, monotone operators and resolvents,
Moreau--Yosida regularization as well as Clarke and (briefly) limiting
subdifferentials. Both first-order (proximal point and splitting) methods and
second-order (semismooth Newton) methods are treated. In addition,
differentiation of set-valued mapping is discussed and used for deriving
second-order optimality conditions for as well as Lipschitz stability
properties of minimizers. Applications to inverse problems and optimal control
of partial differential equations illustrate the derived results and
algorithms. The required background from functional analysis and calculus of
variations is also briefly summarized.
