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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
Nonsmooth Barrier Functions With Applications to Multi-Robot Systems
TL;DR: This letter extends previously established concepts for barrier functions to a class of nonsmooth barrier functions that operate on systems described by differential inclusions, and validates the results by deploying Boolean compositions of nonsMooth Barrier functions onto a team of mobile robots.
Journal ArticleDOI
A critical point theory for nonsmooth functional
Marco Degiovanni,Marco Marzocchi +1 more
TL;DR: In this article, a new generalized notion of ∥df(u)∥ is introduced, which allows to prove several results of critical point theory for continuous functionals, including variational inequalities.
Journal ArticleDOI
Examples when nonlinear model predictive control is nonrobust
TL;DR: It is shown, by examples, that when the optimization problem involves state constraints, or terminal constraints coupled with short optimization horizons, the asymptotic stability of the closed loop may have absolutely no robustness.
Journal ArticleDOI
A General Class of Adaptive Strategies
Sergiu Hart,Andreu Mas-Colell +1 more
TL;DR: In this article, the authors characterize a class of simple adaptive strategies, in the repeated play of a game, having the Hannanconsistency property: in the long run, the player is guaranteed an average payoff as large as the best-reply payoff to the empirical distribution of play of the other players; i.e., there is no regret.
Proceedings Article
300 years of optimal control: From the brachystochrone to the maximum principle
TL;DR: An historical review of the development of optimal control from the publication of the brachystochrone problem by Johann Bernoulli in 1696 can be found in this paper, where ideas on curve minimization already known at the time are briefly outlined.