Results 91 to 100 of about 128 (114)
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Quasidifferential calculus and first-order optimality conditions in nonsmooth optimization
Mathematical Programming Studies, 1986This paper is concerned with first-order optimality conditions for nonsmooth extremal problems. The author first studies positively homogeneous functions (differences of sublinear functions) which are used later in local approximations and difference convex domains.
Shapiro Alexander
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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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Siberian Mathematical Journal, 1988
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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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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Necessary conditions for an extremum in the calculus of variations with nonsmooth phase variables
Mathematical Notes, 1997Weak and strong local minimum for a general isoperimetric problem are studied. Necessary conditions not involving partial derivatives with respect to phase variables are obtained. The results are justified by problems that are not smooth with respect to phase variables.
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Nonconvex-Nonsmooth Calculus of Variations
2001Daniel Goeleven, Dumitru Motreanu
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