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A Relaxed Version of the Cutting Method with Approximation of the Constraint Region
Учёные записки Казанского университета: Серия Физико-математические наукиA cutting method was proposed for solving the convex programming problem. The method assumes that the constraint region of the problem is embedded into some polyhedral sets for constructing iteration points.
I. Ya. Zabotin +2 more
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Weakened subdifferentials and Frechet differentiability of real functions [PDF]
Let X be a real Banach space and f : X ! R [ {+1}. It is well known that the Clarke subdifferential @ f(x) of the function f at x 2 int dom f is a singleton if and only if f is strongly differentiable (then @ f(x) = {Dsf(x)}, where Dsf(x) is the strong ...
Ginchev Ivan
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Inexact Inertial Proximal Algorithm for Maximal Monotone Operators
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2015 In this paper, convergence of the sequence generated by the inexact form of the inertial proximal algorithm is studied. This algorithm which is obtained by the discretization of a nonlinear oscillator with damping dynamical system, has been introduced by
Khatibzadeh Hadi, Ranjbar Sajad
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Homological differential calculus
, 2019 This article provides a definition of a subdifferential for continuous functions based on homological considerations. We show that it satisfies all the requirement for a good notion of subdifferential.
Vichery, Nicolas
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Electronic Journal of Qualitative Theory of Differential Equations, 2005 We investigate the existence of local approximate and strong solutions for a time-dependent subdifferential evolution inclusion with a nonconvex upper-semicontinuous perturbation.
S. Guillaume, A. Syam
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Periodic solutions for time-dependent subdifferential evolution inclusions
, 2017 We consider evolution inclusions driven by a time dependent subdifferential plus a multivalued perturbation. We look for periodic solutions. We prove existence results for the convex problem (convex valued perturbation), for the nonconvex problem ...
Nikolaos S. Papageorgiou +1 more
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On the use of semi-closed sets and functions in convex analysis
Open Mathematics, 2015 The main aim of this short note is to show that the subdifferentiability and duality results established by Laghdir (2005), Laghdir and Benabbou (2007), and Alimohammady et al. (2011), stated in Fréchet spaces, are consequences of the corresponding known
Zălinescu Constantin
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A viability result for second-order differential inclusions
Electronic Journal of Differential Equations, 2002 We prove a viability result for the second-order differential inclusion $$ x''in F(x,x'),quad (x(0), x'(0))=(x_0,y_0)in Q:=Kimes Omega, $$ where $K$ is a closed and $Omega$ is an open subsets of $mathbb{R}^m$, and is an upper semicontinuous set-valued ...
Vasile Lupulescu
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Electronic Journal of Differential Equations, 2013 In this article, we study the existence of an infinite number of subharmonic periodic solutions to a class of second-order neutral nonlinear functional differential equations.
Xiao-Bao Shu, Yongzeng Lai, Fei Xu
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Abstract and Applied Analysis, 2014 We mainly present several equivalent characterizations of the strong metric subregularity of the Mordukhovich subdifferential for an extended-real-valued lower semicontinuous, prox-regular, and subdifferentially continuous function acting on an Asplund ...
J. J. Wang, W. Song
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