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Nonsmooth analysis in measurement processing
Measurement Techniques, 2009It 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
2014A 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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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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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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1984
This survey of nonsmooth analysis sets out to prove an inverse function theorem for set-valued maps. The inverse function theorem for the more usual smooth maps plays a very important role in the solution of many problems in pure and applied analysis, and we can expect such an adaptation of this theorem also to be of great value. For example, it can be
Aubin, J.-P., Ekeland, I.
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This survey of nonsmooth analysis sets out to prove an inverse function theorem for set-valued maps. The inverse function theorem for the more usual smooth maps plays a very important role in the solution of many problems in pure and applied analysis, and we can expect such an adaptation of this theorem also to be of great value. For example, it can be
Aubin, J.-P., Ekeland, I.
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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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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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Elements from Nonsmooth Analysis
2012The main subject of this book is the study of certain classes of nonsmooth equations. An unrenounceable device for the local analysis of smooth equations is the implicit function theorem. This theorem, however, exploits the approximation properties of the derivative of a smooth function and is thus not applicable in the nonsmooth case.
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Nonsmooth analysis and parametric optimization
1990In an optimization problem that depends on parameters, an important issue is the effect that perturbations of the parameters can have on solutions to the problem and their associated multipliers. Under quite broad conditions the possibly multi-valued mapping that gives these elements in terms of the parameters turns out to enjoy a property of “proto ...
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