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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
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Journal ArticleDOI
Regularity Properties of a Semismooth Reformulation of Variational Inequalities
TL;DR: A new reformulation of the KKT conditions for the variational inequality as a system of equations is proposed and a new characterization of strong regularity of KKT points is given.
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Finite-time semistability, Filippov systems, and consensus protocols for nonlinear dynamical networks with switching topologies
TL;DR: In this article, the authors extend the theory of semistability to discontinuous autonomous dynamical systems and present distributed nonlinear static and dynamic output feedback controller architectures for multiagent network consensus and rendezvous with dynamically changing communication topologies.
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Tame functions are semismooth
TL;DR: This work proves that locally Lipschitz functions definable in an o-minimal structure (in particular semialgebraic or globally subanalytic functions) are semismooth and proves that the error at the kth step of the Newton method behaves like O(2^{-{(1+\gamma)}^k}).
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Proximal point method for a special class of nonconvex functions on Hadamard manifolds
TL;DR: In this article, the proximal point method for finding minima of a special class of nonconvex functions on a Hadamard manifold is presented, and it is proved that each accumulation point of this sequence satisfies the necessary optimality conditions.
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On second-order sufficient optimality conditions for c 1,1-optimization problems
Diethard Klatte,K. Tammek +1 more
TL;DR: In this paper, the authors present sufficient conditions for a stationary solution to be isolated or to be a strict local minimizer for C 1.1 functions with locally Lipschitzian gradient mapping.