Sublinear convergence rates of extragradient-type methods: A survey on classical and recent developments

Q Tran-Dinh - arXiv preprint arXiv:2303.17192, 2023 - arxiv.org
The extragradient (EG), introduced by GM Korpelevich in 1976, is a well-known method to
approximate solutions of saddle-point problems and their extensions such as variational …

Strong convergence of forward–reflected–backward splitting methods for solving monotone inclusions with applications to image restoration and optimal control

C Izuchukwu, S Reich, Y Shehu, A Taiwo - Journal of Scientific Computing, 2023 - Springer
In this paper, we propose and study several strongly convergent versions of the forward–
reflected–backward splitting method of Malitsky and Tam for finding a zero of the sum of two …

Extragradient-Type Methods with Last-Iterate Convergence Rates for Co-Hypomonotone Inclusions

Q Tran-Dinh - arXiv preprint arXiv:2302.04099, 2023 - arxiv.org
We develop two" Nesterov's accelerated" variants of the well-known extragradient method to
approximate a solution of a co-hypomonotone inclusion constituted by the sum of two …

Backward-forward-reflected-backward splitting for three operator monotone inclusions

J Rieger, MK Tam - Applied Mathematics and Computation, 2020 - Elsevier
In this work, we propose and analyse two splitting algorithms for finding a zero of the sum of
three monotone operators, one of which is assumed to be Lipschitz continuous. Each …

A product space reformulation with reduced dimension for splitting algorithms

R Campoy - Computational Optimization and Applications, 2022 - Springer
In this paper we propose a product space reformulation to transform monotone inclusions
described by finitely many operators on a Hilbert space into equivalent two-operator …

An inexact Halpern iteration for with application to distributionally robust optimization

L Liang, KC Toh, JJ Zhu - arXiv preprint arXiv:2402.06033, 2024 - arxiv.org
The Halpern iteration for solving monotone inclusion problems has gained increasing
interests in recent years due to its simple form and appealing convergence properties. In this …

Iterative regularization methods with new stepsize rules for solving variational inclusions

D Van Hieu, PK Anh, LD Muu, JJ Strodiot - Journal of Applied …, 2022 - Springer
The paper concerns with three iterative regularization methods for solving a variational
inclusion problem of the sum of two operators, the one is maximally monotone and the …

Stochastic variance-reduced forward-reflected methods for root-finding problems

Q Tran-Dinh - arXiv preprint arXiv:2406.00937, 2024 - arxiv.org
We develop two novel stochastic variance-reduction methods to approximate a solution of
root-finding problems applicable to both equations and inclusions. Our algorithms leverage …

New accelerated splitting algorithm for monotone inclusion problems

LO Jolaoso, Y Shehu, HK Xu - Optimization, 2023 - Taylor & Francis
Forward-reflected-backward splitting algorithm with inertial extrapolation of two inertial
effects to find a zero of the sum of a maximal monotone and a Lipschitz continuous …

Strengthened splitting methods for computing resolvents

FJ Aragón Artacho, R Campoy, MK Tam - Computational Optimization and …, 2021 - Springer
In this work, we develop a systematic framework for computing the resolvent of the sum of
two or more monotone operators which only activates each operator in the sum individually …