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Optimization and nonsmooth analysis
TLDR
The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.Abstract:
1. Introduction and Preview 2. Generalized Gradients 3. Differential Inclusions 4. The Calculus of Variations 5. Optimal Control 6. Mathematical Programming 7. Topics in Analysis.read more
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Journal ArticleDOI
Monotone multigrid methods for elliptic variational inequalities I
TL;DR: It is shown that fast solvers for discrete elliptic variational inequalities of the first kind (obstacle problems) as resulting from the approximation of related continuous problems by piecewise linear finite elements are derived by using basic ideas of successive subspace correction.
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Error Bounds: Necessary and Sufficient Conditions
TL;DR: In this article, a general classification scheme of necessary and sufficient criteria for the error bound property of extended real-valued functions on a Banach space is presented, incorporating the existing conditions.
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Feedback Stabilization and Lyapunov Functions
TL;DR: Given a locally defined, nondifferentiable but Lipschitz Lyapunov function, it is established that the feedback in question possesses a robustness property relative to measurement error, despite the fact that it may not be continuous.
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A Sampling Theory for Compact Sets in Euclidean Space
TL;DR: A parameterized notion of feature size is introduced that interpolates between the minimum of the local feature size and the recently introduced weak feature size to ensure the topological correctness of a reconstruction given by an offset of the sampling.