  These lecture notes for a graduate course cover generalized derivative
concepts useful in deriving necessary optimality conditions and numerical
algorithms for nondifferentiable optimization problems in inverse problems,
imaging, and PDE-constrained optimization. Treated are convex functions and
subdifferentials, Fenchel duality, monotone operators and resolvents,
Moreau--Yosida regularization, proximal point and (some) first-order splitting
methods, Clarke subdifferentials, and semismooth Newton methods. The required
background from functional analysis and calculus of variations is also briefly
summarized.
