A NOTE ON THE DIFFERENTIABILITY OF CONVEX-FUNCTIONS [PDF]
, 1994 Every real-valued convex and locally Lipschitzian function f defined on a nonempty closed convex set D of a Banach space E is the local restriction of a convex Lipschitzian function defined on E. Moreover, if E is separable and int D not-equal empty set,
Cheng, L. X., Wu, C. X., 程立新
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Clarke Subgradients for Directionally Lipschitzian Stratifiable Functions [PDF]
Mathematics of Operations Research, 2015 Using a geometric argument, we show that under a reasonable continuity condition, the Clarke subdifferential of a semi-algebraic (or more generally stratifiable) directionally Lipschitzian function admits a simple form: The normal cone to the domain and limits of gradients generate the entire Clarke subdifferential.
Dmitriy Drusvyatskiy +2 more
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From Lipschitzian to non-Lipschitzian characteristics: continuity of behaviors [PDF]
, 2000 Linear complementarity systems are used to model discontinuous dynamical systems such as networks with ideal diodes and mechanical systems with unilateral constraints.
Camlibel, M.K. +8 more
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Demonstratio Mathematica, 2020 In this article, we present a sufficient condition about the length of the interval for the existence and uniqueness of mild solutions to a fractional boundary value problem with Sturm-Liouville boundary conditions when the data function is of ...
Harjani Jackie +2 more
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Existence results for ABC-fractional BVP via new fixed point results of F-Lipschitzian mappings
Demonstratio Mathematica, 2022 In this article, fixed point results for self-mappings in the setting of two metrics satisfying FF-lipschitzian conditions of rational-type are proved, where FF is considered as a semi-Wardowski function with constant τ∈R\tau \in {\mathbb{R}} instead of ...
Mehmood Nayyar +3 more
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Iteration Functions in Some Nonsmooth Optimization Algorithms [PDF]
, 1997 In this paper, it is proved that a locally Lipschitzian function has a PHR iteration function or a QS iteration function if and only if it is pseudo-regular, and a locally Lipschitzian function has a positive homogeneous PHR iteration function or a ...
Liu, Guoshan
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Existence of solutions for a second order boundary value problem with the Clarke subdifferential [PDF]
, 2017 In this paper, we prove a theorem on the existence of solutions for a second order differential inclusion governed by the Clarke subdifferential of a Lipschitzian function and by a mixed semicontinuous perturbation.
Samira Melit, Dalila Azzam-Laouir
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The alpha algorithm and the application of the cubic algorithm in case of unknown Lipschitz constant [PDF]
, 1993 A new algorithm for full global optimization of a Lipschitzian function over an arbitrary bounded set in Rn is presented. A procedure is proposed to handle functions with unknown Lip constants. Application to the cubic algorithm is given and illustrative
Galperin, E.A.
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A New Quadrature Rule Derived from Spline Interpolation with Error Analysis [PDF]
, 2011 We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose ...
Hadi Taghvafard
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First- and second-order directional differentiability of locally Lipschitzian functions [PDF]
, 2008 In this paper, characterizations of the existence of the directional derivative and second-order parabolic directional derivative of a locally Lipschitzian function are established.
Ward, D.E.
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