Results 21 to 30 of about 659 (80)
On the linear convergence of the stochastic gradient method with constant step-size [PDF]
, 2018 The strong growth condition (SGC) is known to be a sufficient condition for linear convergence of the stochastic gradient method using a constant step-size $\gamma$ (SGM-CS).
Cevher, Volkan, Vu, Bang Cong
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Iterative solution of unstable variational inequalities on approximately given sets
Abstract and Applied Analysis, Volume 1, Issue 1, Page 45-64, 1996., 1996 The convergence and the stability of the iterative regularization method for solving variational inequalities with bounded nonsmooth properly monotone (i.e., degenerate) operators in Banach spaces are studied. All the items of the inequality (i.e., the operator A, the “right hand side” f and the set of constraints Ω) are to be perturbed. The connection
Y. I. Alber, A. G. Kartsatos, E. Litsyn
wiley +1 more source
Asymptotic behavior of solutions of nonlinear functional differential equations
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 703-712, 1994., 1994 Using the properties of almost nonexpansive curves introduced by B. Djafari Rouhani, we study the asymptotic behavior of solutions of nonlinear functional differential equation du(t)/dt + Au(t) + G(u)(t)?f(t), where A is a maximal monotone operator in a Hilbert space H, f?L1(0, 8 : H) and is a given mapping.
Jong Soo Jung +2 more
wiley +1 more source
Rectangularity and paramonotonicity of maximally monotone operators [PDF]
, 2012 Maximally monotone operators play a key role in modern optimization and variational analysis. Two useful subclasses are rectangular (also known as star monotone) and paramonotone operators, which were introduced by Brezis and Haraux, and by Censor, Iusem
Bauschke, Heinz H. +2 more
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Nonlinear random operator equations and inequalities in Banach spaces
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 1, Page 111-118, 1992., 1990 In this paper we give some new existence theorems for nonlinear random equations and inequalities involving operators of monotone type in Banach spaces. A random Hammerstein integral equation is also studied. In order to obtain random solutions we use some results from the existing deterministic theory as well as from the theory of measurable ...
Antonios Karamolegos +1 more
wiley +1 more source
Fixed points in the family of convex representations of a maximal monotone operator
, 2008 Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation.
Svaiter, B. F.
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Convex KKM maps, monotone operators and Minty variational inequalities
, 2015 It is known that for convex sets, the KKM condition is equivalent to the finite intersection property. We use this equivalence to obtain a characterisation of monotone operators in terms of convex KKM maps and in terms of the existence of solutions to ...
Lassonde, Marc
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On relationships between two linear subspaces and two orthogonal projectors
Special Matrices, 2019 Sum and intersection of linear subspaces in a vector space over a field are fundamental operations in linear algebra. The purpose of this survey paper is to give a comprehensive approach to the sums and intersections of two linear subspaces and their ...
Tian Yongge
doaj +1 more source
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 In this paper, in the setting of Hadamard spaces, a iterative scheme is proposed for approximating a solution of the inclusion problem for a finite family of monotone operators which is a unique solution of a variational inequality.
Ranjbar Sajad
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Strong convergence for the modified Mann's iteration of $\lambda$-strict pseudocontraction
, 2014 In this paper, for an $\lambda$-strict pseudocontraction $T$, we prove strong convergence of the modified Mann's iteration defined by $$x_{n+1}=\beta_{n}u+\gamma_nx_n+(1-\beta_{n}-\gamma_n)[\alpha_{n}Tx_n+(1-\alpha_{n})x_n],$$ where $\{\alpha_{n}\}$, $ \{
Song, Yisheng, Wang, Hongjun
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