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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
Control of nonlinear variable structure systems
Giorgio Bartolini,T Zolezzi +1 more
TL;DR: In this paper, the extension de la theorie des systemes de commande discontinue a structure variable a quelques cas non lineaires, which is the same variable used in this paper.
Journal ArticleDOI
Mobility of bodies in contact. II. How forces are generated by curvature effects
Elon Rimon,J.W. Burdick +1 more
TL;DR: Using configuration-space based elastic deformation models, it is shown that any object which is kinematically immobilized to first or second-order is also dynamically locally asymptotically stable with respect to perturbations.
Book ChapterDOI
DC Programming and DCA for General DC Programs
TL;DR: A natural extension of DC programming and DCA for modeling and solving general DC programs with DC constraints is presented, and two resulting approaches consist in reformulating those programs as standard DC programs in order to use standard DCAs for their solutions.
Journal ArticleDOI
On relaxed constant rank regularity condition in mathematical programming
TL;DR: It is shown that the relaxed CRCQ (and, consequently, CRCQ too) implies the R-regularity (in other terms the error bound property) of a system of inequalities and equalities and it is proved that the constant positive linear dependence condition also implies R- regularity.
Journal ArticleDOI
Dynamic hemivariational inequality modeling viscoelastic contact problem with normal damped response and friction
TL;DR: In this article, a multidimensional hemivariational inequality is proposed to describe the dynamic contact of a viscoelastic body and a foundation, which is modeled by a general normal damped response condition and a friction law, which are nonmonotone, possibly multivalued and have the subdifferential form.