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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
Optimal Feedback Control: Foundations, Examples, and Experimental Results for a New Approach
TL;DR: A sampling theorem is developed that indicates that the Lipschitz constant of the dynamics is a fundamental sampling frequency and leads to a new set of foundations for achieving feedback wherein optimality principles are interwoven to achieve stability and system performance.
Journal ArticleDOI
New types of variational principles based on the notion of quasidifferentiability
TL;DR: In this article, several new types of variational principles derived by using the new mathematical notion of quasidifferentiability were derived by means of V. F. Dem'yanov.
Journal ArticleDOI
Nonmonotone Trust-Region Methods for Bound-Constrained Semismooth Equations with Applications to Nonlinear Mixed Complementarity Problems
TL;DR: It is proved that close to a regular solution the trust-region algorithm turns into this projected Newton method, which is shown to converge locally q-superlinearly or quadratically, respectively, depending on the quality of the approximate subdifferentials used.
Journal ArticleDOI
Navigation of Multiple Kinematically Constrained Robots
TL;DR: A new nonsmooth backstepping controller is introduced for translating kinematic controllers to equivalent dynamic ones, while maintaining bounded velocity specifications.
Proceedings ArticleDOI
Exact cellular decompositions in terms of critical points of Morse functions
TL;DR: In this paper, the authors define exact cellular decompositions where critical points of Morse functions indicate the location of cell boundaries, and derive a general framework for defining decomposition in terms of critical points.