Results 211 to 220 of about 22,103,434 (252)

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.
R. Tyrrell Rockafellar, Alan J. King
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Impacts on Nonsmooth Analysis [PDF]

, 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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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.
Luis T. Aguilar, Yury Orlov
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Nonsmooth analysis in measurement processing

Measurement Techniques, 2009
It is shown that processing dynamic measurements is an inverse problem in relation to cause-effect consequences and belongs to the class of turning-point methods, while nonsmooth analysis provides the necessary conditions for a minimum in the error functional in the form of a combined maximum principle.
A. A. Kostoglotov, S. V. Lazarenko
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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].
Dumitru Motreanu, Vicenţiu D. Rădulescu   +1 more
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Convergence and rate analysis of a proximal linearized ADMM for nonconvex nonsmooth optimization

Journal of Global Optimization, 2022
Maryam Yashtini
semanticscholar   +1 more source

Elements of Nonsmooth Analysis

1993
The 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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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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Variational pairs and applications to stability in nonsmooth analysis

Nonlinear Analysis: Theory, Methods & Applications, 2002
In the paper, it is pointed out that many of the basic results of nonsmooth analysis (e.g., subdifferential calculus, mean-value inequalities and optimality conditions) can be derived directly by general variational principles. In this manner, the authors provide a general definition of a variational pair \((X,\delta)\) where \(X\) is a complete metric
D. Azè, J. Corvellec, LUCCHETTI, ROBERTO   +2 more
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Variational and Monotonicity Methods in Nonsmooth Analysis

Frontiers in Mathematics, 2021
Nicuşor Costea, A. Kristály, C. Varga
semanticscholar   +1 more source