Results 71 to 80 of about 683 (180)
An Extragradient Method for Fixed Point Problems and Variational Inequality Problems
Journal of Inequalities and Applications, 2007 We present an extragradient method for fixed point problems and variational inequality problems. Using this method, we can find the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality
Yonghong Yao +2 more
doaj +2 more sources
Journal of Mathematics, Volume 2024, Issue 1, 2024.This paper aims to introduce an iterative algorithm based on an inertial technique that uses the minimum number of projections onto a nonempty, closed, and convex set. We show that the algorithm generates a sequence that converges strongly to the common solution of a variational inequality involving inverse strongly monotone mapping and fixed point ...
Watanjeet Singh +2 more
wiley +1 more source
MathematicsThis research focuses on developing a novel approach to finding fixed points of quasi-nonexpansive mappings without relying on the demi-closedness condition, a common requirement in previous studies. The approach is based on the Subgradient Extragradient
Anchalee Sripattanet, Atid Kangtunyakarn
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Open Journal of Mathematical Optimization, 2022 In this short note, we provide a simple version of an accelerated forward-backward method (a.k.a. Nesterov’s accelerated proximal gradient method) possibly relying on approximate proximal operators and allowing to exploit strong convexity of the ...
Barré, Mathieu +2 more
doaj +1 more source
The Extragradient (EG) method stands as a cornerstone algorithm for solving monotone nonlinear equations but faces two important unresolved challenges: (i) how to select stepsizes without relying on the global Lipschitz constant or expensive line-search procedures, and (ii) how to reduce the two full evaluations of the mapping required per iteration to
Liu, Xiaozhi, Xia, Yong
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Revisiting Stochastic Extragradient [PDF]
, 2019 We consider a new extension of the extragradient method that is motivated by approximating implicit updates. Since in a recent work~\cite{chavdarova2019reducing} it was shown that the existing stochastic extragradient algorithm (called mirror-prox) of ...
Kovalev, Dmitry +4 more
core
Mathematics, 2020 We introduce a new projection and contraction method with inertial and self-adaptive techniques for solving variational inequalities and split common fixed point problems in real Hilbert spaces.
Lateef Olakunle Jolaoso, Maggie Aphane
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Revisiting Stochastic Extragradient [PDF]
, 2020 We fix a fundamental issue in the stochastic extragradient method by providing a new sampling strategy that is motivated by approximating implicit updates.
Kovalev, Dmitry +4 more
core
Relative Lipschitzness in Extragradient Methods and a Direct Recipe for Acceleration
CoRR, 2020 We show that standard extragradient methods (i.e. mirror prox and dual extrapolation) recover optimal accelerated rates for first-order minimization of smooth convex functions. To obtain this result we provide a fine-grained characterization of the convergence rates of extragradient methods for solving monotone variational inequalities in terms of a ...
Cohen, Michael B. +2 more
openaire +4 more sources
The modified extragradient method for nonexpansive multivalued mappings and variational inequality problems [PDF]
, 2019 [[abstract]]In this paper, we prove the strong convergence of an approximating common element of the set of fixed points of a nonexpansive multivalued mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz ...
Thatsawan Homhual +2 more
core