Results 171 to 180 of about 1,716 (212)

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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Optimality Conditions for Maximizing a Locally Lipschitz Function

Optimization, 2005
In this article we intend to study the necessary and sufficient conditions for global maximization of locally Lipschitz functions. We develop a necessary and sufficient condition for a class of Lipschitz pseudoconvex function in terms of the Clarke subdifferential. We also develop sufficient conditions for optimality in terms of very general non-smooth
Joydeep Dutta
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A (CF)-mapping of integral functional of locally lipschitz functions

Journal of Global Optimization, 2006
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On Characterization of Convexity for Regularly Locally Lipschitz Functions

Nonlinear Analysis: Theory, Methods & Applications, 2004
The authors provide a characterization of convexity for regularly locally Lipschitz functions on Banach spaces by means of a special kind of a second-order upper Dini directional derivative. Let \(X\) be a real Banach space and \(f: X\to\mathbb{R}\) be a locally Lipschitz function. The function \(f\) is assumed to be regular, i.e., the Dini directional
Karel Pastor
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Geometric conditions of differentiability for a regular locally Lipschitz function

Acta Mathematica Sinica, 1998
Summary: The differentiability of a norm of a Banach space may be characterized by its unit sphere. This paper generalizes these geometric conditions of differentiability of the norm to the case of regular locally Lipschitz functions.
Shi, Shuzhong, Wang, Bingwu
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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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A Bundle Trust Region Algorithm for Minimizing Locally Lipschitz Functions

SIAM Journal on Optimization, 2023
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Sierpiński's hierarchy and locally Lipschitz functions

Fundamenta Mathematicae, 1995
Let \(Z\) be an uncountable Polish space and let \(S_\alpha (Z)\) \((\alpha < \omega_1)\) be classes of functions \(g : Z \to R\) \((R\) -- the real line) of Sierpiński classification of Borel measurable functions. A function \(f : I \to R\) \((I\) -- an interval in \(R)\) is said to be locally Lipschitz on \(I\) if for each point \(x\) in \(I\) there ...
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Line Search Algorithms for Locally Lipschitz Functions on Riemannian Manifolds

SIAM Journal on Optimization, 2018
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S. Hosseini, W. Huang, R. Yousefpour
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An Algorithm for Minimizing a Class of Locally Lipschitz Functions

Journal of Optimization Theory and Applications, 1996
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L S Zhang, X L Sun
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