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Optimization and nonsmooth analysis
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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
Citations
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Journal ArticleDOI
A vector forward mode of automatic differentiation for generalized derivative evaluation
Kamil A. Khan,Paul I. Barton +1 more
TL;DR: It is shown here that piecewise differentiable functions are lexicographically smooth in the sense of Nesterov, and that lexicographic derivatives of these functions comprise a particular subset of both the B-subdifferential and the Clarke Jacobian.
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Nonpathological Lyapunov functions and discontinuous Carathéodory systems
TL;DR: For these equations, sufficient conditions which guarantee both Lyapunov stability and asymptotic stability in terms of nonsmooth LyAPunov functions are given and an invariance principle is also proven.
Journal ArticleDOI
Globally Convergent Variable Metric Method for Nonconvex Nondifferentiable Unconstrained Minimization
TL;DR: In this paper, a special variable metric method is given for finding the stationary points of locally Lipschitz continuous functions which are not necessarily convex or differentiable time consuming quadratic programming subproblems do not need to be solved.
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Uncertainty in Mechanism Design
TL;DR: In this article, the authors consider mechanism design problems with Knightian uncertainty formalized using incomplete preferences, and show that full extraction is generically possible with maximal incentive compatible mechanisms, but requires sufficient disagreement across types.
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Brief paper: Nonsmooth optimization for multiband frequency domain control design
Pierre Apkarian,Dominikus Noll +1 more
TL;DR: This work extends previous work on nonsmooth H"~ synthesis to develop a nonsm Smooth optimization technique to compute local solutions to multiband synthesis problems.