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The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…

Numerical Analysis · Mathematics 2022-10-26 Petr N. Vabishchevich

We investigate the asymptotic behavior of a stochastic version of the forward-backward splitting algorithm for finding a zero of the sum of a maximally monotone set-valued operator and a cocoercive operator in Hilbert spaces. Our general…

Optimization and Control · Mathematics 2015-07-28 Patrick L. Combettes , Jean-Christophe Pesquet

In this work we study operator splitting methods for a certain class of coupled abstract Cauchy problems, where the coupling is such that one of the problems prescribes a "boundary type" extra condition for the other one. The theory of…

Analysis of PDEs · Mathematics 2021-05-21 Petra Csomós , Matthias Ehrhardt , Bálint Farkas

This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general…

Optimization and Control · Mathematics 2017-11-07 Renato D. C. Monteiro , Chee-Khian Sim

Many parallel algorithms which solve basic problems in computer science use auxiliary space linear in the input to facilitate conflict-free computation. There has been significant work on improving these parallel algorithms to be in-place,…

Data Structures and Algorithms · Computer Science 2025-03-11 Chase Hutton , Adam Melrod

We consider the following general scheduling problem: The input consists of n jobs, each with an arbitrary release time, size, and a monotone function specifying the cost incurred when the job is completed at a particular time. The…

Data Structures and Algorithms · Computer Science 2010-08-31 Nikhil Bansal , Kirk Pruhs

Operator splitting methods allow to split the operator describing a complex dynamical system into a sequence of simpler subsystems and treat each part independently. In the modeling of dynamical problems, systems of (possibly coupled)…

Dynamical Systems · Mathematics 2023-09-01 Andreas Bartel , Malak Diab , Andreas Frommer , Michael Günther

It is common to encounter large-scale monotone inclusion problems where the objective has a finite sum structure. We develop a general framework for variance-reduced forward-backward splitting algorithms for this problem. This framework…

Machine Learning · Statistics 2021-03-17 Xun Zhang , William B. Haskell , Zhisheng Ye

In this article, we use the monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems and especially in the case that the objective…

Optimization and Control · Mathematics 2020-03-26 Tran Ngoc Thang , Vijender Kumar Solanki , Tuan Anh Dao , Nguyen Thi Ngoc Anh , Hai V. Pham

We focus on the linear convergence of generalized proximal point algorithms for solving monotone inclusion problems. Under the assumption that the associated monotone operator is metrically subregular or that the inverse of the monotone…

Optimization and Control · Mathematics 2022-03-29 Hui Ouyang

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

Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal…

Machine Learning · Computer Science 2021-11-23 Kai Yan , Jie Yan , Chuan Luo , Liting Chen , Qingwei Lin , Dongmei Zhang

We introduce the first operator splitting method for composite monotone inclusions outside of Hilbert spaces. The proposed primal-dual method constructs iteratively the best Bregman approximation to an arbitrary point from the Kuhn-Tucker…

Optimization and Control · Mathematics 2015-09-10 Patrick L. Combettes , Quang Van Nguyen

In this paper, we propose a randomized intertial block-coordinate primaldual fixed point algorithm to solve a wide array of monotone inclusion problems base on the modification of the heavy ball method of Nesterov. These methods rely on a…

Optimization and Control · Mathematics 2016-11-17 Meng Wen , Shigang Yue , Yuchao Tan , Jigen Peng

We study stochastic monotone inclusion problems, which widely appear in machine learning applications, including robust regression and adversarial learning. We propose novel variants of stochastic Halpern iteration with recursive variance…

Optimization and Control · Mathematics 2023-01-10 Xufeng Cai , Chaobing Song , Cristóbal Guzmán , Jelena Diakonikolas

Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately.…

Neural and Evolutionary Computing · Computer Science 2026-04-17 Liam Wigney , Frank Neumann

This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…

Numerical Analysis · Mathematics 2024-05-08 Sergio Blanes , Fernando Casas , Ander Murua

In this article we present a modified S-iteration process that we combine with inertial extrapolation to find a common solution to the split monotone inclusion problem and the fixed point problem in real Hilbert space.Our goal is to…

Numerical Analysis · Mathematics 2021-10-11 Shamshad Husain , Uqba Rafat

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 a numerical approach for solving composite primal-dual monotone inclusions with a priori information. The underlying a priori information set is represented by the intersection of fixed point sets of a finite…

Optimization and Control · Mathematics 2020-11-06 Luis Briceño-Arias , Julio Deride , Cristian Vega