Results 211 to 220 of about 3,785 (249)

The best possible estimates for polynomial norms on certain LP—spaces

, 1984
Sarantopoulos, I
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Locally Lipschitz Functionals

2021
In this chapter we focus our attention on the theory developed by Clarke for locally Lipschitz functionals. More precisely, we will investigate the properties of the generalized directional derivative and the Clarke subdifferential as well as the connection with the convex subdifferential.
Nicuşor Costea, Alexandru Kristály, Csaba Varga   +2 more
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On implicit function theorem for locally Lipschitz equations

Mathematical Programming, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aram V. Arutyunov, Sergey E. Zhukovskiy
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Semigroups of locally Lipschitz operators.

Mathematical Journal of Okayama University, 2002
The infinitesimal generators of semigroups of locally Lipschitz operators are characterized. An application of the obtained result is given to the Cauchy problem for the Kirchhoff equation with real analytic initial data.
Kobayashi, Yoshikazu, Tanaka, Naoki
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Local Minimality of a Lipschitz Extremal

Canadian Journal of Mathematics, 1992
AbstractIn this paper the question of weak and strong local optimality of a Lipschitz (as opposed to C1 ) extremal is addressed. We show that the classical Jacobi sufficient conditions can be extended to the case of Lipschitz candidates. The key idea for this achievement lies in proving that the “generalized” strengthened Weierstrass condition is ...
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Lipschitz classes on local fields

Science in China Series A: Mathematics, 2007
The Lipschitz class Lipα on a local field K is defined in this note, and the equivalent relationship between the Lipschitz class Lipα and the Holder type space C α (K) is proved. Then, those important characteristics on the Euclidean space R n and the local field K are compared, so that one may interpret the essential ...
Wei-yi Su, Guo-xiang Chen
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Local Lipschitz-constant Functions and Maximal Subdifferentials

Set-Valued Analysis, 2003
Let \(X\) be a Banach space. For the study of generalized subdifferentials, the authors introduce the notion of topologically robust upper semicontinuity for real-valued functions. So the function \(k(x)\) is called to be topologically robust usc if it is upper semicontinuous and quasi lower semicontinuous.
Borwein, J. M., Vanderwerff, J., Wang, Xianfu   +2 more
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On conditions to have bounded multipliers in locally lipschitz programming

Mathematical Programming, 1980
For a nonlinear programming problem with locally Lipschitz objective and inequality constraint functions and continuously differentiable equality constraint functions, a necessary and sufficient condition is presented for the set of multiplier vectors to be nonempty and bounded.
Nguyen, Van Hien, Strodiot, Jean-Jacques, Mifflin, Robert   +2 more
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An Effective Nonsmooth Optimization Algorithm for Locally Lipschitz Functions

Journal of Optimization Theory and Applications, 2012
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Nezam Mahdavi-Amiri, Rohollah Yousefpour
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New constructions for local approximation of Lipschitz functions. I

Nonlinear Analysis: Theory, Methods & Applications, 2003
In a former paper, the author presented a new generalized differentiability notion for Lipschitz functions \(f: \mathbb{R}^n\to\mathbb{R}\) according to \[ \begin{multlined} Df(x_0)= \text{conv}\Biggl\{v\in\mathbb{R}^n\mid\exists g\in \mathbb{R}^n,\| g\|= 1,\exists r(x_0,\cdot,g)\in \eta(x_0),\;\exists\alpha_k\to +0:\\ v= \lim_{k\to\infty}\,{1\over ...
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