Results 141 to 150 of about 226 (176)

Isolated zeros of lipschitzian metrically regular -Functions

Optimization, 2001
Given a metrically regular locally Lipschitzian function sending into ,the structure of the preimages will be studied. In particular, for the case of m =n, it will be shown that all preimages are locally finite sets provided that the Lipschitzian function in question is directionally differentiable.
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Lipschitzian composition operators in some function spaces

Nonlinear Analysis: Theory, Methods & Applications, 1997
There are several function spaces \(X\) with the property that, whenever the Nemytskij operator \(F\phi(x)= f(x,\phi(x))\) is Lipschitz continuous in the norm of \(X\), the generating function \(f\) must be affine, i.e. \(f(x, y)= g(x)y+ h(x)\) with \(g,h\in X\). For example, in case \(X= \text{Lip}\) by the author [Funkc. Ekvacioj Ser. Int.
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Lipschitzian norms and functional inequalities for birth-death processes

Discrete and Continuous Dynamical Systems - B, 2023
This paper treats a birth-death process with generator \({\mathcal L}\) and reversible invariant probability measure \(\pi\). The author identifies explicitly the Lipschitzian norm of the solution of the Poisson equation \(- {\mathcal L} G = g - \pi(g)\) for \(\vert g \vert \leqslant \varphi\). This leads to some transportation-information inequalities,
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Locally lipschitzian guiding function method for ODEs

Nonlinear Analysis: Theory, Methods & Applications, 1998
The author treats the existence of periodic solutions to the problem \[ x'(t) = f(t,x(t)), \quad x(0)=x(T), \tag{*} \] where \(f:[0,T] \times \mathbb{R}^n \to \mathbb{R}^n\) is a Carathéodory function with integrably bound growth. Under the assumption that \(f\) has a locally Lipschitzian guiding function \(V\) with Ind\((V) \neq 0\) it is proved that ...
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Subgradient of distance functions with applications to Lipschitzian stability

Mathematical Programming, 2005
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Mordukhovich, Boris S., Nam, Nguyen Mau
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The Lipschitzianity of convex vector and set-valued functions

TOP, 2015
Let \(X,Y\) be normed spaces and \(C\) a proper convex cone in \(Y\) inducing an order relation \(\leq_C\) on \(Y\). One puts \(Y^\bullet=Y\cup\{+\infty\}\), where \(+\infty\) is an ideal element attached to \(Y\) such that \(y\leq_C+\infty\) for all \(y\in Y\). The \(C\)-convexity of a function \(f:X\to Y^\bullet\) is defined in the usual way by using
Vu Anh Tuan, Tammer, Christiane, Zălinescu, Constantin   +2 more
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Discrete maximum principle for problems with lipschitzian functions

International Journal of Control, 1988
The objective of this paper is to present the discrete maximum principle for problems with mixed equality and inequality constraints on state and control. The functions under consideration are locally lipschitzian. Two versions of the discrete maximum principle are given.
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When is any continuous function Lipschitzian?

1998
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Lipschitzian inverse functions, directional derivatives, and applications inC 1,1 optimization

Journal of Optimization Theory and Applications, 1991
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Solution of monotone complementarity problems with locally Lipschitzian functions

Mathematical Programming, 1997
The paper deals with complementarity problems CP(F), where the underlying function F is assumed to be locally Lipschitzian. Based on a special equivalent reformulation of CP(F) as a system of equations (Phi)(x) = 0 or as the problem of minimizing the merit function (psi) =1/2 ^ 2_2, we extend results which hold for sufficiently smooth functions F to ...
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