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The classical Krasnoselskii-Mann iteration is broadly used for approximating fixed points of nonexpansive operators. To accelerate the convergence of the Krasnoselskii-Mann iteration, the inertial methods were received much attention in…

Functional Analysis · Mathematics 2020-01-09 Fuying Cui , Yang Yang , Yuchao Tang , Chuanxi Zhu

For solving structured monotone inclusion problems involving the sum of finitely many maximal monotone operators, we propose and study a relative-error inertial-relaxed inexact projective splitting algorithm. The proposed algorithm benefits…

Optimization and Control · Mathematics 2023-01-25 M. Marques Alves , Marina Geremia , Raul T. Marcavillaca

In this paper, we first propose a general inertial proximal point method for the mixed variational inequality (VI) problem. Based on our knowledge, without stronger assumptions, convergence rate result is not known in the literature for…

Optimization and Control · Mathematics 2014-08-04 Caihua Chen , Shiqian Ma , Junfeng Yang

This work focuses on convergence analysis of the projected gradient method for solving constrained convex minimization problem in Hilbert spaces. We show that the sequence of points generated by the method employing the Armijo linesearch…

Optimization and Control · Mathematics 2015-08-10 Jose Yunier Bello Cruz , Welington de Oliveira

Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies…

Optimization and Control · Mathematics 2021-05-18 Patrick L. Combettes , Zev C. Woodstock

The article is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Starting from the recently proposed proximal variant of the extragradient method for this class…

Optimization and Control · Mathematics 2023-08-02 S. S. Ablaev , F. S. Stonyakin , M. S. Alkousa , D. A. Pasechnyuk

Projective splitting is a family of methods for solving inclusions involving sums of maximal monotone operators. First introduced by Eckstein and Svaiter in 2008, these methods have enjoyed significant innovation in recent years, becoming…

Optimization and Control · Mathematics 2020-02-19 Patrick R. Johnstone , Jonathan Eckstein

We establish linear convergence rates for a certain class of extrapolated fixed point algorithms which are based on dynamic string-averaging methods in a real Hilbert space. This applies, in particular, to the extrapolated simultaneous and…

Optimization and Control · Mathematics 2018-05-11 Christian Bargetz , Victor I. Kolobov , Simeon Reich , Rafał Zalas

The article is devoted to the development of numerical methods for solving variational inequalities with relatively strongly monotone operators. We consider two classes of variational inequalities related to some analogs of the Lipschitz…

Optimization and Control · Mathematics 2022-05-25 F. S. Stonyakin , A. A. Titov , D. V. Makarenko , M. S. Alkousa

In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…

Exactly Solvable and Integrable Systems · Physics 2007-11-16 Dan Butnariu , Gabor Kassay

We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…

Optimization and Control · Mathematics 2023-11-03 Angelia Nedich , Tatiana Tatarenko

We propose an inertial variant of the strongly convergent inexact proximal-point (PP) method of Solodov and Svaiter (2000) for monotone inclusions. We prove strong convergence of our main algorithm under less restrictive assumptions on the…

Optimization and Control · Mathematics 2025-09-24 M. Marques Alves , J. E. Navarro Caballero , M. Geremia , R. T. Marcavillaca

In the context of convex optimization problems in Hilbert spaces, we induce inertial effects into the classical ADMM numerical scheme and obtain in this way so-called inertial ADMM algorithms, the convergence properties of which we…

Optimization and Control · Mathematics 2014-04-18 Radu Ioan Bot , Ernö Robert Csetnek

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…

Optimization and Control · Mathematics 2011-01-10 Luis M. Briceño-Arias

In this paper, we propose an inertial accelerated primal-dual method for the linear equality constrained convex optimization problem. When the objective function has a ``nonsmooth + smooth'' composite structure, we further propose an…

Optimization and Control · Mathematics 2021-06-30 Xin He , Rong Hu , Ya-Ping Fang

We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…

Optimization and Control · Mathematics 2020-01-30 Mootta Prangprakhon , Nimit Nimana , Narin Petrot

In this paper an inexact proximal point method for variational inequalities in Hadamard manifolds is introduced and studied its convergence properties. The main tool used for presenting the method is the concept of enlargement of monotone…

Optimization and Control · Mathematics 2015-11-30 E. E. A. Batista , G. C. Bento , O. P. Ferreira

In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under…

Optimization and Control · Mathematics 2026-01-27 Pavel Dvurechensky , Meggie Marschner , Shimrit Shtern , Mathias Staudigl

In this paper, we propose an inertial forward backward splitting algorithm to compute a zero of the sum of two monotone operators, with one of the two operators being co-coercive. The algorithm is inspired by the accelerated gradient method…

Computer Vision and Pattern Recognition · Computer Science 2014-09-15 Dirk A. Lorenz , Thomas Pock

The aim of this paper is to study the weak convergence analysis of sequence of iterates generated by a three-operator splitting method of Davis and Yin incorporated with two-step inertial extrapolation for solving monotone inclusion problem…

Optimization and Control · Mathematics 2024-10-03 Olaniyi S. Iyiola , Lateef O. Jolaoso , Yekini Shehu