Results 1 to 10 of about 1,369 (204)
Characterization of Strict Convexity for Locally Lipschitz Functions
Rocky Mountain Journal of Mathematics, 2009 It is well known that a smooth function \(f: X\to\mathbb{R}\) is convex iff \(f''(x;h, h)\geq 0\) for all \(x\in X\) and all \(h\in X\). The function \(f\) is strictly convex iff \(f''(x;h,h)> 0\) for ``almost'' all \(x\in X\) and all \(h\in X\). Here \[ f''(x;u,v)= \lim_{t\to 0} \frac{\langle\nabla f(x+ tu)-\nabla f(x),v\rangle}{t}, \] where \(\nabla ...
Karel Pastor
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The oscillation of separately locally Lipschitz functions
Karpatsʹkì Matematičnì Publìkacìï, 2011 We prove that a function which dened on the product of two metric Baire spaces is the oscillation of some separately locally Lipschitz function if and only if it is an upper semicontinuous non-negative function which has a crosswise nowhere dense closure
V. H. Herasymchuk, O. V. Maslyuchenko
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Abstract and Applied Analysis, 2019 We define and study C1-solutions of the Aronsson equation (AE), a second order quasi linear equation. We show that such super/subsolutions make the Hamiltonian monotone on the trajectories of the closed loop Hamiltonian dynamics. We give a short, general
Pierpaolo Soravia
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A new trust region method for minimizing locally lipschitz functions [PDF]
تصمیم گیری و تحقیق در عملیات, 2020 In this paper, we present a new trust region method for unconstrained optimization problems with locally Lipschitz continuous, nonconvex functions. In this method, in the ratio test, the current objective function value is replaced with maximum of some ...
Zohreh Akbari
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Abstract and Applied Analysis, 2022 In this paper, we establish a generalization of the Galewski-Rădulescu nonsmooth global implicit function theorem to locally Lipschitz functions defined from infinite dimensional Banach spaces into Euclidean spaces.
Guy Degla +2 more
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Limitations of Local Filters of Lipschitz and Monotone Functions [PDF]
ACM Transactions on Computation Theory, 2012 We study local filters for two properties of functions of the form f : {0,1}d → R: the Lipschitz property and monotonicity. A local filter with additive error a is a randomized algorithm that is given black-box access to a function f and a query point x
Pranjal Awasthi +3 more
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Lq-Estimates for stationary Stokes system with coefficients measurable in one direction [PDF]
Bulletin of Mathematical Sciences, 2019 We study the stationary Stokes system with variable coefficients in the whole space, a half space, and on bounded Lipschitz domains. In the whole and half spaces, we obtain a priori Ẇq1-estimates for any q ∈ [2,∞) when the coefficients are merely ...
Hongjie Dong, Doyoon Kim
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An extension of the quasi-Newton method for minimizing locally Lipschitz functions [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2019 We present a method to minimize locally Lipschitz functions. At first, a local quadratic model is developed to approximate a locally Lipschitz function. This model is constructed by using the ϵ-subdifferential.
Z. Akbari
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On error bound moduli for locally Lipschitz and regular functions [PDF]
Mathematical Programming, 2017 In this paper we study local error bound moduli for a locally Lipschitz and regular function via its outer limiting subdifferential set. We show that the distance of 0 from the outer limiting subdifferential of the support function of the subdifferential set, which is essentially the distance of 0 from the end set of the subdifferential set, is an ...
M. H. Li, K. W. Meng, Xiaoqi Yang 0001
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Periodic solutions for a differential inclusion problem involving the p(t)-Laplacian
Advances in Nonlinear Analysis, 2020 In the present paper, we consider the nonlinear periodic systems involving variable exponent driven by p(t)-Laplacian with a locally Lipschitz nonlinearity.
Chen Peng, Tang Xianhua
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