Results 61 to 70 of about 290 (158)
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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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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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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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
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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
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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
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A Strongly Convergent Method for the Split Feasibility Problem
Abstract and Applied Analysis, 2012 The purpose of this paper is to introduce and analyze a strongly convergent method which combined regularized method, with extragradient method for solving the split feasibility problem in the setting of infinite-dimensional Hilbert spaces. Note that the
Yonghong Yao +2 more
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A new self-adaptive method for solving resolvent of sum of two monotone operators in Banach spaces
Fixed Point Theory and Algorithms for Sciences and Engineering, 2023 We introduce a Tseng extragradient method for solving monotone inclusion problem in Banach space. A strong convergence result of an Halpern inertial extrapolation method for solving the resolvent of sum of two monotone operators without the knowledge of ...
H. A. Abass, M. Aphane, O. K. Oyewole
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Abstract and Applied Analysis, 2012 We suggest and analyze a modified extragradient method for solving variational inequalities, which is convergent strongly to the minimum-norm solution of some variational inequality in an infinite-dimensional Hilbert space.
Yonghong Yao +2 more
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Low-rank extragradient methods for scalable semidefinite optimization
Operations Research LettersWe consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in statistics, machine learning, combinatorial optimization, and other domains.
Dan Garber, Atara Kaplan
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