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 …
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
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 …
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 …
approximate a solution of a co-hypomonotone inclusion constituted by the sum of two …
Backward-forward-reflected-backward splitting for three operator monotone inclusions
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 …
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 …
described by finitely many operators on a Hilbert space into equivalent two-operator …
An inexact Halpern iteration for with application to distributionally robust optimization
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 …
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 …
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 …
root-finding problems applicable to both equations and inclusions. Our algorithms leverage …
New accelerated splitting algorithm for monotone inclusion problems
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 …
effects to find a zero of the sum of a maximal monotone and a Lipschitz continuous …
Strengthened splitting methods for computing resolvents
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 …
two or more monotone operators which only activates each operator in the sum individually …