Nonsmooth Analysis and Optimization

Christian Clason

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arXiv · 1708.04180

Nonsmooth Analysis and Optimization

Christian Clason

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Abstract

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.

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Christian Clason. 2017-08-14. Nonsmooth Analysis and Optimization. https://arxiv.org/abs/1708.04180

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