Results 91 to 100 of about 7,741 (135)
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Subdifferential Calculus and Nonsmooth Critical Point Theory
SIAM Journal on Optimization, 2000Summary: A general critical point theory for continuous functions defined on metric spaces has been recently developed. A new subdifferential, related to that theory, is introduced. In particular, results on the subdifferential of a sum are proved. An example of application to PDEs is sketched.
Campa, Ines, Degiovanni, Marco
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Journal of Nonlinear and Variational Analysis, 2023
Summary: To deal with nondifferentiable interval-valued functions (IVFs) (not necessarily convex), we present the notion of Fréchet subdifferentiability or \(gH\)-Fréchet subdifferentiability. We explore its relationship with \(gH\)-differentiability and develop various calculus results for \(gH\)-Fréchet subgradients of extended IVFs.
Kumar, Gourav, Yao, Jen-Chih
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Summary: To deal with nondifferentiable interval-valued functions (IVFs) (not necessarily convex), we present the notion of Fréchet subdifferentiability or \(gH\)-Fréchet subdifferentiability. We explore its relationship with \(gH\)-differentiability and develop various calculus results for \(gH\)-Fréchet subgradients of extended IVFs.
Kumar, Gourav, Yao, Jen-Chih
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Variational sets: Calculus and applications to nonsmooth vector optimization
Nonlinear Analysis: Theory, Methods & Applications, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hoang Anh, Nguyen Le +2 more
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Generalized Euler–Lagrange equation for nonsmooth calculus of variations
Nonlinear Dynamics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Skandari, M. H. Noori +2 more
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2016
*In this chapter we provide an overview of the main aspects of the mooth and nonsmooth calculus. We start with the smooth calculus and we introduce the notions of Gâteaux and Frechet derivatives. We develop all the important calculus rules and we present the implicit and inverse function theorems together with their most important consequences. Then we
Leszek Gasiński +1 more
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*In this chapter we provide an overview of the main aspects of the mooth and nonsmooth calculus. We start with the smooth calculus and we introduce the notions of Gâteaux and Frechet derivatives. We develop all the important calculus rules and we present the implicit and inverse function theorems together with their most important consequences. Then we
Leszek Gasiński +1 more
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Nonsmooth Calculus of Semismooth Functions and Maps
Journal of Optimization Theory and Applications, 2013The author considers the relationship between semismooth sets on one hand and semismooth mappings and their epigraphs on the other hand. Furthermore, it is shown that the Mordukhovich and linear subdifferential (coderivative) for semismooth functions (vector-valued maps) are the same.
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Siberian Mathematical Journal, 1989
The variational problem in a Sobolev space is considered, i.e. \[ J_ F(u)=\int_{G}F[x,u(x),u'(x)]dx\to \inf, \] where the function F(x,s,\(\cdot)\) is convex for all x,s. The authors show that if u is a minimizer then there is a function h: \(G\times {\mathbb{R}}\to {\mathbb{R}}^ n\) such that \[ \int_{G}\{\frac{\partial F}{\partial S}[x,u(x),u'(x ...
Reshetnyak, Yu. G., Kudryavtseva, N. A.
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The variational problem in a Sobolev space is considered, i.e. \[ J_ F(u)=\int_{G}F[x,u(x),u'(x)]dx\to \inf, \] where the function F(x,s,\(\cdot)\) is convex for all x,s. The authors show that if u is a minimizer then there is a function h: \(G\times {\mathbb{R}}\to {\mathbb{R}}^ n\) such that \[ \int_{G}\{\frac{\partial F}{\partial S}[x,u(x),u'(x ...
Reshetnyak, Yu. G., Kudryavtseva, N. A.
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Directional Derivative Calculus and Optimality Conditions in Nonsmooth Mathematical Programming
Journal of Information and Optimization Sciences, 1989Abstract Recent research in nonsmooth analysis has produced a calculus for generalized directional derivatives and subgradients of nondifferentiable functions.
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Nonsmoothness and nonconvexity in calculus of variations and optimal control
Proceedings of 1994 33rd IEEE Conference on Decision and Control, 2002We discuss a number of questions relating to the modern theory of necessary conditions in optimal control: Is the Euler-Lagrange inclusion necessary for a weak minimum? In case of nonconvex dependence, does there exist an adjoint arc satisfying jointly the Euler-Lagrange inclusion and the Weierstrass-type condition?
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Corrigendum to "Convex Subcones of the Contingent Cone in Nonsmooth Calculus and Optimization"
Transactions of the American Mathematical Society, 1989This is a correction to the paper ibid. 302, 661-682 (1987; Zbl 0629.58007).
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