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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{
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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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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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Sensitivity analysis of nonsmooth power control systems with an example of wind turbines
Communications in Nonlinear Science and Numerical Simulation, 2021Peter Stechlinski, Sameh A Eisa
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