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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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On the Clarke subdifferential of the distance function of a closed set
TL;DR: In this article, the extent to which formulas for the Clarke subdifferential of the distance for C, d c (x) := inf y ∈c ‖x − y − y, which are valid when C is convex, remain valid if C is not convex.
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Variational structure and multiple solutions for a fractional advection-dispersion equation
TL;DR: By establishing a variational structure and using the critical point theory, the existence of multiple solutions for a class of fractional advection-dispersion equations arising from a symmetric transition of the mass flux is investigated.
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Optimal bounds for the effective energy of a mixture of isotropic, incompressible, elastic materials
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Distributed motion constraints for algebraic connectivity of robotic networks
TL;DR: A distributed coordination algorithm is proposed that allows the robots to decide whether a desired collective motion breaks connectivity and a secondcoordination algorithm is built on this procedure to design a second coordination algorithm that allowsThe robots to modify a wanted collective motion to guarantee that connectivity is preserved.