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IoT-enabled real-time health monitoring system for adolescent physical rehabilitation. [PDF]

Sci Rep
Yang J, Hu J, Chen W.
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Analysis and Optimization of Nonsmooth Arches

SIAM Journal on Control and Optimization, 2002
The Kirchoff-Love model for a smooth clamped arch is considered first. A new treatment for that classical model is developed. A variational formulation, based on optimal control theory, is introduced and, using duality-type arguments, the deformation of the arches are explicitly expressed by integral formulas.
Sprekels, Jürgen, Ignat, Anca, Tiba, Dan   +2 more
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Nonsmooth analysis of eigenvalues

Mathematical Programming, 1999
Subdifferentials (limiting Fréchet, Clarke) of the composition \(f\circ \lambda \) of extended real valued permutation invariant functions \(f\) and the eigenvalue vector function \(\lambda \) of a symmetric matrix \(X\) are calculated using the transformation to principles axes.
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Lidskii's Theorem via Nonsmooth Analysis

SIAM Journal on Matrix Analysis and Applications, 2000
Summary: Lidskii's theorem on eigenvalue perturbation is proved via a nonsmooth mean value theorem.
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Nonsmooth Analysis in Control Theory: A Survey

European Journal of Control, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Elements of Nonsmooth Analysis

2003
In this Chapter we recall important definitions and results from the theory of generalized gradient for locally Lipschitz functionals due to Clarke [8], different nonsmooth versions of Palais-Smale conditions and basic elements of nonsmooth calculus developed by Degiovanni [9], [10].
D. Motreanu, V. Rădulescu
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Sensitivity analysis for nonsmooth generalized equations

Mathematical Programming, 1992
In this paper a generalized parametric equation (1) \(0\in f(p,x)+N(x)\), where \(f\) is a given function from \(\Omega\times \mathbb{R}^ n\) to \(\mathbb{R}^ m\), \(N\) a multifunction from \(\mathbb{R}^ n\) to \(\mathbb{R}^ m\), and \(p\) an element of an open subset \(\Omega\) of a normed linear space, is considered.
Alan J. King, R. Tyrrell Rockafellar
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Elements of Nonsmooth Analysis

2014
A differential construct that applies to nonsmooth functions is useful in general. The proximal supergradient admits a very complete calculus for upper semicontinuous functions and perfectly suits the nonsmooth \(\mathcal{L}_{2}\)-gain analysis to be developed in this chapter.
Yury V. Orlov, Luis T. Aguilar
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Adjoint Coexhausters in Nonsmooth Analysis and Extremality Conditions

Journal of Optimization Theory and Applications, 2012
The article of M. E. Abbasov and V. F. Demyanov is a valuable contribution to the field of nondifferentiable or nonsmooth calculus and, especially, optimization. This investigation takes place in a wide analytic setting, in the tradition of the quasidifferential which it extends and employs.
Majid E. Abbasov, Vladimir F. Demyanov
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Impacts on Nonsmooth Analysis

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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