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We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An important feature of the algorithm is that the…

Optimization and Control · Mathematics 2011-08-09 Patrick L. Combettes , Jean-Christophe Pesquet

In this paper we provide an algorithm for solving constrained composite primal-dual monotone inclusions, i.e., monotone inclusions in which a priori information on primal-dual solutions is represented via closed convex sets. The proposed…

Optimization and Control · Mathematics 2018-05-31 Luis Briceño-Arias , Sergio López Rivera

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 iteration of these algorithms require one forward evaluation…

Optimization and Control · Mathematics 2020-01-22 Janosch Rieger , Matthew K. Tam

The averaged alternating modified reflections algorithm is a projection method for finding the closest point in the intersection of closed convex sets to a given point in a Hilbert space. In this work, we generalize the scheme so that it…

Optimization and Control · Mathematics 2024-01-03 F. J. Aragón Artacho , R. Campoy

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

We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by…

Optimization and Control · Mathematics 2012-06-27 Radu Ioan Bot , Ernö Robert Csetnek , Andre Heinrich

We propose an inertial Douglas-Rachford splitting algorithm for finding the set of zeros of the sum of two maximally monotone operators in Hilbert spaces and investigate its convergence properties. To this end we formulate first the…

Optimization and Control · Mathematics 2014-03-31 Radu Ioan Bot , Ernö Robert Csetnek , Christopher Hendrich

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

Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion,…

Optimization and Control · Mathematics 2020-06-24 Minh N. Bùi , Patrick L. Combettes

The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some…

Functional Analysis · Mathematics 2013-07-30 Radu Ioan Bot , Christopher Hendrich

For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…

Optimization and Control · Mathematics 2026-03-25 Geng-Hua Li , Hai-Yi Zhao , Xiangkai Sun

We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces. We…

Optimization and Control · Mathematics 2017-05-08 Radu Ioan Bot , Ernö Robert Csetnek

We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in \cite{vu} for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators…

Optimization and Control · Mathematics 2013-03-13 Radu Ioan Bot , Ernö Robert Csetnek , Andre Heinrich

In this paper we provide a splitting method for finding a zero of the sum of a maximally monotone operator, a lipschitzian monotone operator, and a normal cone to a closed vectorial subspace of a real Hilbert space. The problem is…

Optimization and Control · Mathematics 2014-06-25 Luis M. Briceño-Arias

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

We introduce a dynamical system to the problem of finding zeros of the sum of two maximally monotone operators. We investigate the existence, uniqueness and extendability of solutions to this dynamical system in a Hilbert space. We prove…

Classical Analysis and ODEs · Mathematics 2021-08-17 Ewa M. Bednarczuk , Raj Narayan Dhara , Krzysztof E. Rutkowski

We introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for…

Functional Analysis · Mathematics 2017-01-20 K. R. Kazmi , Mohd Furkan

We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…

Optimization and Control · Mathematics 2012-06-29 Patrick L. Combettes , Bang C. Vũ

This work is devoted to establish the strong convergence results of an iterative algorithm generated by the shrinking projection method in Hilbert spaces. The proposed approximation sequence is used to find a common element in the set of…

Functional Analysis · Mathematics 2018-03-07 Abdul Ghaffar , Zafar Ullah , Muhammad Aqeel Ahmad Khan , Faisal Mumtaz

We consider resolvent splitting algorithms for finding a zero of the sum of finitely many maximally monotone operators. The standard approach to solving this type of problem involves reformulating as a two-operator problem in the…

Optimization and Control · Mathematics 2024-12-18 Farhana A. Simi , Matthew K. Tam