نتایج جستجو برای: locally lipschitz mapping

تعداد نتایج: 283166  

2004
D. AUSSEL

Prox-regularity of a set (Poliquin-Rockafellar-Thibault, 2000), or its global version, proximal smoothness (Clarke-Stern-Wolenski, 1995) plays an important role in variational analysis, not only because it is associated with some fundamental properties as the local continuous differentiability of the function dist (C; ·), or the local uniqueness of the projection mapping, but also because in th...

Journal: :Journal of Geometric Analysis 2023

We extend the definition of involutivity to non-Lipschitz tangent subbundles using generalized functions. prove Frobenius Theorem with sharp regularity estimate when subbundle is log-Lipschitz: if $${\mathcal {V}}$$ a log-Lipschitz involutive rank r, then for any $$\varepsilon >0$$ , locally there homeomorphism $$\Phi (u,v)$$ such that ,\frac{\partial \Phi }{\partial u^1},\dots u^r}\in C^{0,1-\...

2011
Nicolas BOULEAU

be locally Lipschitz. This occurs in particular when d — 1. In that case it is possible to construct almost sure and L approximations X'(u>) of X(u>) by approximating the Brownian path u> and using the continuity of the Ito mapping (see e.g. [6] [28] [21]). Actually, with or without the Frobenius assumption, direct discretization schemes X' can be constructed which converge in V and for some sc...

2007
CLARA LÖH ROMAN SAUER

The simplicial volume introduced by Gromov provides a topologically accessible lower bound for the minimal volume. Lafont and Schmidt proved that the simplicial volume of closed, locally symmetric spaces of noncompact type is positive. In this paper, we extend this positivity result to certain non-compact locally symmetric spaces of finite volume, including Hilbert modular varieties. The key id...

2012
W. HARE C. SAGASTIZÁBAL M. SOLODOV

We consider the problem of computing a critical point of a nonconvex locally Lipschitz function over a convex compact constraint set given an inexact oracle that provides an approximate function value and an approximate subgradient. We assume that the errors in function and subgradient evaluations are merely bounded, and in particular need not vanish in the limit. After some discussion on how t...

2014
P. GROHS S. HOSSEINI

This paper presents a Riemannian trust region algorithm for unconstrained optimization problems with locally Lipschitz objective functions defined on complete Riemannian manifolds. To this end we define a function Φ : TM → R on the tangent bundle TM , and at k-th iteration, using the restricted function Φ|TxkM where TxkM is the tangent space at xk, a local model function Qk that carries both fi...

Journal: :Optimization Methods and Software 2017
Frank E. Curtis Tim Mitchell Michael L. Overton

We propose an algorithm for solving nonsmooth, nonconvex, constrained optimization problems as well as a new set of visualization tools for comparing the performance of optimization algorithms. Our algorithm is a sequential quadratic optimization method that employs BFGS quasi-Newton Hessian approximations and an exact penalty function whose parameter is controlled using a steering strategy. We...

Journal: :Axioms 2012
Emil Saucan Meir Katchalski

We investigate the interplay between the existence of fat triangulations, PL approximations of Lipschitz–Killing curvatures and the existence of quasiconformal mappings. In particular we prove that if there exists a quasiconformal mapping between two PL or smooth n-manifolds, then their Lipschitz–Killing curvatures are bilipschitz equivalent. An extension to the case of almost Riemannian manifo...

2010
Kazimierz Goebel Brailey Sims

Lipschitz self mappings of metric spaces appear in many branches of mathematics. In this paper we introduce a modification of the Lipschitz condition which takes into account not only the mapping itself but also the behaviour of a finite number of its iterates. We refer to such mappings as mean Lipschitzian. The study of this new class of mappings seems potentially interesting and leads to some...

2011
LU-CHUAN CENG QAMRUL HASAN ANSARI NGAI-CHING WONG JEN-CHIH YAO

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of a variational inequality problem for a monotone and Lipschitz continuous mapping. We introduce an extragradient-like iterative algorithm that is based on the extragradient-like a...

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