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In this paper, we propose and study the iteration complexity of an inexact Douglas-Rachford splitting (DRS) method and a Douglas-Rachford-Tseng's forward-backward (F-B) splitting method for solving two-operator and four-operator monotone…

Optimization and Control · Mathematics 2017-12-01 M. Marques Alves , M. Geremia

In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower semi-continuous while the other is differentiable with a…

Optimization and Control · Mathematics 2016-10-28 Jingwei Liang , Jalal Fadili , Gabriel Peyré

This paper is concerned with convex composite minimization problems in a Hilbert space. In these problems, the objective is the sum of two closed, proper, and convex functions where one is smooth and the other admits a computationally…

Optimization and Control · Mathematics 2020-02-19 Patrick R. Johnstone , Pierre Moulin

Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…

Machine Learning · Computer Science 2023-10-27 Xufeng Cai , Ahmet Alacaoglu , Jelena Diakonikolas

We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusion in real Hilbert space. The algorithm allows to use the inexact computations of the Lipschitzian and cocoercive…

Optimization and Control · Mathematics 2024-01-11 Vu Cong Bang , Dimitri Papadimitriou , Vu Xuan Nham

In this article we provide a splitting method for solving monotone inclusions in a real Hilbert space involving four operators: a maximally monotone, a monotone-Lipschitzian, a cocoercive, and a monotone-continuous operator. The proposed…

Optimization and Control · Mathematics 2022-07-20 Luis Briceño-Arias , Fernando Roldán

We study frugal splitting algorithms with minimal lifting for solving monotone inclusion problems involving sums of maximal monotone and cocoercive operators. Building on a foundational result by Ryu, we fully characterize all methods that…

Optimization and Control · Mathematics 2025-04-16 Anton Åkerman , Enis Chenchene , Pontus Giselsson , Emanuele Naldi

In this paper we propose a new fast splitting algorithm to solve the Weighted Split Bregman minimization problem in the backward step of an accelerated Forward-Backward algorithm. Beside proving the convergence of the method, numerical…

Numerical Analysis · Mathematics 2018-10-01 D. Lazzaro , E. Loli Piccolomini , F. Zama

In this paper, we present a convergence rate analysis for the inexact Krasnosel'skii-Mann iteration built from nonexpansive operators. Our results include two main parts: we first establish global pointwise and ergodic iteration-complexity…

Optimization and Control · Mathematics 2015-09-17 Jingwei Liang , Jalal Fadili , Gabriel Peyré

We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…

Optimization and Control · Mathematics 2015-12-31 J. Y. Bello Cruz , R. Diaz Millan

In this paper, we present a stochastic forward-backward-half forward splitting algorithm with variance reduction for solving the structured monotone inclusion problem composed of a maximally monotone operator, a maximally monotone operator…

Optimization and Control · Mathematics 2025-06-10 Liqian Qin , Yaxuan Zhang , Qiao-Li Dong , Michael Th. Rassias

In this paper, a conceptual algorithm modifying the forward-backward-half-forward (FBHF) splitting method for solving three operator monotone inclusion problems is investigated. The FBHF splitting method adjusts and improves Tseng's…

Optimization and Control · Mathematics 2021-04-28 Yunier Bello-Cruz , Oday Hazaimah

We propose an extended forward-backward algorithm for approximating a zero of a maximal monotone operator which can be split as the extended sum of two maximal monotone operators. We establish the weak convergence in average of the sequence…

Optimization and Control · Mathematics 2013-06-25 Marc Lassonde , Ludovic Nagesseur

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

Optimization and Control · Mathematics 2016-05-30 James Renegar

Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…

Functional Analysis · Mathematics 2024-03-18 Guillermina Fongi , María Celeste Gonzalez

We propose and analyze a versatile and general algorithm called nonlinear forward-backward splitting (NOFOB). The algorithm consists of two steps; first an evaluation of a nonlinear forward-backward map followed by a relaxed projection onto…

Optimization and Control · Mathematics 2021-01-25 Pontus Giselsson

This paper introduces generalized Bregman projection algorithms for solving nonlinear split feasibility problems (SF P s) in infinitedimensional Hilbert spaces. The methods integrate Bregman projections, proximal gradient steps, and…

Optimization and Control · Mathematics 2025-05-20 Saeed Hashemi Sababe , Ehsan Lotfali Ghasab

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

We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…

Machine Learning · Statistics 2020-07-13 Riccardo Grazzi , Luca Franceschi , Massimiliano Pontil , Saverio Salzo

Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…

Numerical Analysis · Computer Science 2018-06-11 Ganzhao Yuan , Wei-Shi Zheng , Li Shen , Bernard Ghanem