Introduction to Nonsmooth Analysis and Optimization [article]

Christian Clason, Tuomo Valkonen
2020 arXiv   pre-print
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
more » ... 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. The required background from functional analysis and calculus of variations is also briefly summarized.
arXiv:2001.00216v3 fatcat:gs342de7v5eb3bfkxhdmxosyim