Distributed convex optimization via proportional-integral-differential algorithm
Measurement + Control, 2022 This paper studies the distributed convex optimization problem, where the global utility function is the sum of local cost functions associated to the individual agents.
Wei Zhu, Haibao Tian
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Existence of fixed points on compact epilipschitz sets without invariance conditions
Fixed Point Theory and Applications, 2005 We provide a new result of existence of equilibria of a single-valued Lipschitz function f on a compact set K of â„Ân which is locally the epigraph of a Lipschitz functions (such a set is called epilipschitz set).
Marc Quincampoix, Mikhail Kamenskii
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The oscillation of separately locally Lipschitz functions
Karpatsʹkì Matematičnì Publìkacìï, 2013 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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Discretization methods for nonconvex differential inclusions
Electronic Journal of Qualitative Theory of Differential Equations, 2009 We prove the existence of solutions for the differential inclusion $\dot x(t)\in F(t,x(t)) + f(t,x(t))$ for a multifunction $F$ upper semicontinuous with compact values contained in the generalized Clarke gradient of a regular locally Lipschitz function ...
M. Yarou
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Some notes on commutators of the fractional maximal function on variable Lebesgue spaces
Journal of Inequalities and Applications, 2019 Let ...
Pu Zhang, Zengyan Si, Jianglong Wu
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2-Local Isometries on Spaces of Lipschitz Functions
Canadian Mathematical Bulletin, 2011 AbstractLet (X, d) be a metric space, and let Lip(X) denote the Banach space of all scalar-valued bounded Lipschitz functions ƒ on X endowed with one of the natural normswhere L(ƒ) is the Lipschitz constant of ƒ. It is said that the isometry group of Lip(X) is canonical if every surjective linear isometry of Lip(X) is induced by a surjective isometry ...
Jiménez Vargas, Antonio +1 more
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Convergence of the Momentum Method for Semialgebraic Functions with Locally Lipschitz Gradients
SIAM Journal on Optimization, 2023 33 pages.
Cédric Josz +2 more
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Some Inexact Version of the Iterative Exponential Method for Solving Nonsmooth Equations
Algorithms, 2023 This paper presents an inexact version of an exponential iterative method designed for solving nonlinear equations F(x)=0, where the function F is only locally Lipschitz continuous.
Marek J. Śmietański
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A Multiplicity Theorem for Locally Lipschitz Periodic Functionals
Journal of Mathematical Analysis and Applications, 1995 The authors consider the periodic multivalued problem of the forced pendulum \[ \begin{cases} x''(t) + f(t)\in \biggl[\underline g\bigl(x(t) \bigr), \overline g \bigl(x(t) \bigr)\biggr], \quad \text{a.e. } t\in(0,1) \\ x(0) = x(1),\;x'(0) = x'(1) \end{cases} \] where \(f\in L^p(0,1)\), \(g\in L^\infty (\mathbb{R})\) is periodic of period \(T\), the ...
Mironescu, P., Radulescu, V.D.
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Local convergence of exact and inexact newton’s methods for subanalytic variational inclusions
Revista de Matemática: Teoría y Aplicaciones, 2015 This paper deals with the study of an iterative method for solving a variational inclusion of the form 0 ∈ f (x)+F (x) where f is a locally Lipschitz subanalytic function and F is a set-valued map from Rn to the closed subsets of Rn.
Catherine Cabuzel +2 more
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