NONSMOOTH ANALYSIS AND OPTIMIZATION
By Christian Clason. 2017
88 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/42de714eeb408b0450a83b773cf0ae0cb3032bc9
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In Applied Mathematics
- Shuicheng Yan
- Reinhard Heckel
- Wen Huang
- Vladislav Voroninski
- Paul Hand
- Canyi Lu
- Zhouchen Lin
- Jinhui Tang
In Computational Theory and Mathematics
- Shuicheng Yan
- Reinhard Heckel
- Wen Huang
- Vladislav Voroninski
- Paul Hand
- Canyi Lu
- Zhouchen Lin
- Jinhui Tang
In Mathematical Physics
Citations in the corpus
- Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm (2015, background): “From the upper semi-continuous property of the subdifferential [42, Proposition 2.1.5], there exists Let t → + ∞ in (30).”
- A Provably Convergent Scheme for Compressive Sensing Under Random Generative Priors (2018, methodology): “Since the cost function f (x) is continuous, piecewise quadratic, and not differentiable everywhere, we use the notion of a generalized gradient, called the Clarke subdifferential or generalized subdifferential [6].”