Results 201 to 210 of about 49,792,933 (254)
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Sensitivity-analysis methods for nonsmooth multibody systems with contact and friction
Multibody system dynamics, 2022Haijun Peng +3 more
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2011
We discuss the notions of regular and critical points/values for nonsmooth functions. The notion of topologically regular points for min-type functions is introduced. It is shown that the level set of a min-type function corresponding to a regular value, is a Lipschitz manifold.
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We discuss the notions of regular and critical points/values for nonsmooth functions. The notion of topologically regular points for min-type functions is introduced. It is shown that the level set of a min-type function corresponding to a regular value, is a Lipschitz manifold.
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Mathematical diagnostics via nonsmooth analysis
Optimization Methods and Software, 2005Mathematical Diagnostics (MD) deals with identification problems arising in different practical areas. In the paper, the problem of the choice of a classifier and a functional is discussed. Existing methods of linear discriminant analysis are based on linear and quadratic programming.
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Nonsmooth Analysis of Lorentz Invariant Functions
SIAM Journal on Optimization, 2007A real valued function $g(x,t)$ on ${\mathbb{R}}^n \times {\mathbb{R}}$ is called a Lorentz invariant if $g(x,t)=g(Ux,t)$ for all $n \times n$ orthogonal matrices U and all $(x,t)$ in the domain of g. In other words, g is invariant under the linear orthogonal transformations preserving the Lorentz cone: $\{(x,t) \in {\mathbb{R}}^n \times {\mathbb{R}} \,
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International Conference on Machine Learning
We investigate the finite-time analysis of finding ($\delta,\epsilon$)-stationary points for nonsmooth nonconvex objectives in decentralized stochastic optimization.
Emre Sahinoglu, Shahin Shahrampour
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We investigate the finite-time analysis of finding ($\delta,\epsilon$)-stationary points for nonsmooth nonconvex objectives in decentralized stochastic optimization.
Emre Sahinoglu, Shahin Shahrampour
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Piecewise Ck functions in nonsmooth analysis
Nonlinear Analysis: Theory, Methods & Applications, 1990We shall examine certain classes of nonsmooth functions which are of interest in nonsmooth analysis and optimization. The functions which we shall consider are termed piecewise \(C^ k\) functions, usually with \(k=1\) or \(k=2\). Roughly speaking, a real-valued function defined on an open subset W of \(R^ n\) is said to be piecewise \(C^ k\) on W if it
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Elements of Nonsmooth Analysis
1993The aim of Chapter 1 is to provide some notions and propositions of Nonsmooth Analysis that will be used in the next Chapters for the study of engineering problems leading to hemivariational inequalities. The propositions are given here without proofs.
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