Results 171 to 180 of about 4,084 (221)

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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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

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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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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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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Mathematical diagnostics via nonsmooth analysis

Optimization Methods and Software, 2005
Mathematical 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, 2007
A 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{
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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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Piecewise Ck functions in nonsmooth analysis

Nonlinear Analysis: Theory, Methods & Applications, 1990
We 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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Nonsmooth Analysis

2023
Piernicola Bettiol, Richard Vinter
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