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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
Finding Optimal Algorithmic Parameters Using Derivative-Free Optimization
Charles Audet,Dominique Orban +1 more
TL;DR: A general framework for identifying locally optimal algorithmic parameters in unconstrained optimization is devised and the derivative-free method chosen to guide the process is the mesh adaptive direct search, a generalization of pattern search methods.
Journal ArticleDOI
Finite-time synchronization of complex networks with nonidentical discontinuous nodes
Xinsong Yang,Zhiyou Wu,Jinde Cao +2 more
TL;DR: New conditions for general discontinuous chaotic systems is proposed, and a set of new controllers are designed such that the considered model can be finite-timely synchronized onto any target node with discontinuous functions.
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Stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple Lyapunov functions
TL;DR: This paper presents a general framework for analyzing stability of nonlinear switched systems, by combining the method of multiple Lyapunov functions with a suitably adapted comparison principle in the context of stability in terms of two measures.
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Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems
Jong-Shi Pang,Defeng Sun,Jie Sun +2 more
TL;DR: It is shown that for a parametric complementarity problem of this kind, if a solution corresponding to a base parameter is strongly stable, then a semismooth implicit solution function exists whose directional derivatives can be computed by solving certain affine problems on the critical cone at the base solution.
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Relaxation of an optimal control problem involving a perturbed sweeping process
J. F. Edmond,Lionel Thibault +1 more
TL;DR: The existence of solutions for perturbed sweeping processes whose perturbations are Lipschitz single-valued maps is established and a relaxation result concerning optimal control problems involving such processes is extended to the infinite dimensional setting.