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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
Vanishing Viscosity Solutions of Nonlinear Hyperbolic Systems
TL;DR: In this paper, the authors consider the Cauchy problem for a strictly hyperbolic, n × n system in one-space dimension, and show that the solutions of the viscous approximations ut + A(u)ux = euxx are defined globally in time and satisfy uniform BV estimates, independent of e.
Book
Large Deviations for Stochastic Processes
Jin Feng,Thomas G. Kurtz +1 more
TL;DR: The general theory of large deviations: Large deviations and exponential tightness Large deviations for stochastic processes, large deviations for Markov processes and semigroup convergence, and nonlinear semiigroup convergence using viscosity solutions is discussed in this article.
Journal ArticleDOI
Exponential stabilization of driftless nonlinear control systems using homogeneous feedback
TL;DR: This paper provides a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers, and can be extended to a large class of systems with torque inputs.
Journal ArticleDOI
On the Rank of Extreme Matrices in Semidefinite Programs and the Multiplicity of Optimal Eigenvalues
TL;DR: It is proved that clustering must occur at extreme points of the set of optimal solutions, if the number of variables is sufficiently large and a lower bound on the multiplicity of the critical eigenvalue is given.
Posted Content
Coordination and geometric optimization via distributed dynamical systems
Jorge E. Cortes,Francesco Bullo +1 more
TL;DR: D dynamical systems for disk-covering and sphere-packing problems are discussed and a collection of distributed control laws that are related to nonsmooth gradient systems are designed and analyzed.