English
Related papers

Related papers: Bregman Monotone Operator Splitting

200 papers

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

This work is concerned with the classical problem of finding a zero of a sum of maximal monotone operators. For the projective splitting framework recently proposed by Combettes and Eckstein, we show how to replace the fundamental…

Optimization and Control · Mathematics 2020-08-24 Patrick R. Johnstone , Jonathan Eckstein

Finding a zero of a sum of maximally monotone operators is a fundamental problem in modern optimization and nonsmooth analysis. Assuming that resolvents of the operators are available, this problem can be tackled with the Douglas-Rachford…

Optimization and Control · Mathematics 2021-09-24 Heinz H. Bauschke , Shambhavi Singh , Xianfu Wang

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

The linear complementarity problem (LCP) is a general set membership problem that includes quadratic cone programming as a special case. In this work we consider a homogeneous embedding of the LCP, which encodes both the optimality…

Optimization and Control · Mathematics 2021-06-15 Brendan O'Donoghue

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

Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are built from sums, linear…

Optimization and Control · Mathematics 2015-07-31 Damek Davis

We consider the problem of minimizing the sum of three functions, one of which is nonconvex but differentiable, and the other two are convex but possibly nondifferentiable. We investigate the Three Operator Splitting method (TOS) of Davis &…

Optimization and Control · Mathematics 2021-06-15 Alp Yurtsever , Varun Mangalick , Suvrit Sra

The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…

Functional Analysis · Mathematics 2019-08-30 Fuying Cui , Yuchao Tang , Chuanxi Zhu

We propose a novel stochastic distributed method for both monotone and strongly monotone variational inequalities with Lipschitz operator and proper convex regularizers arising in various applications from game theory to adversarial…

Optimization and Control · Mathematics 2024-10-07 Aleksandr Beznosikov , Darina Dvinskikh , Dmitry Bylinkin , Andrei Semenov , Alexander Gasnikov

We propose a new primal-dual splitting method for solving composite inclusions involving Lipschitzian, and parallel-sum-type monotone operators. Our approach extends the framework in \cite{Siopt4} to a more general class of monotone…

Optimization and Control · Mathematics 2015-07-28 Quoc Tran-Dinh , Bang Cong Vu

Operator splitting is a popular divide-and-conquer strategy for solving differential equations. Typically, the right-hand side of the differential equation is split into a number of parts that are then integrated separately. Many methods…

Numerical Analysis · Mathematics 2023-08-14 Raymond J. Spiteri , Arash Tavassoli , Siqi Wei , Andrei Smolyakov

A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…

Optimization and Control · Mathematics 2013-03-04 Stephen Becker , M. Jalal Fadili

Monotone inclusions have wide applications in solving various convex optimization problems arising in signal and image processing, machine learning, and medical image reconstruction. In this paper, we propose a new splitting algorithm for…

Optimization and Control · Mathematics 2020-09-29 Hui Yu , Chunxiang Zong , Yuchao Tang

Finding a zero of a sum of maximally monotone operators is a fundamental problem in modern optimization and nonsmooth analysis. Assuming that the resolvents of the operators are available, this problem can be tackled with the…

Optimization and Control · Mathematics 2025-07-31 Heinz H. Bauschke , Shambhavi Singh , Xianfu Wang

Minimizing sum of two functions under a linear constraint is what we called splitting problem. This convex optimization has wide applications in machine learning problems, such as Lasso, Group Lasso and Sparse logistic regression. A recent…

Computation · Statistics 2017-11-20 Sen Na , Cho-Jui Hsieh

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

Operator splitting techniques have recently gained popularity in convex optimization problems arising in various control fields. Being fixed-point iterations of nonexpansive operators, such methods suffer many well known downsides, which…

Optimization and Control · Mathematics 2020-04-01 Andreas Themelis , Panagiotis Patrinos

We develop a novel stochastic primal dual splitting method with Bregman distances for solving a structured composite problems involving infimal convolutions in non-Euclidean spaces. The sublinear convergence in expectation of the…

Optimization and Control · Mathematics 2021-03-17 Nguyen Van Dung , Băng Công Vũ

In this work, we propose a new splitting algorithm for solving structured monotone inclusion problems composed of a maximally monotone operator, a maximally monotone and Lipschitz continuous operator and a cocoercive operator. Our method…

Optimization and Control · Mathematics 2025-11-07 Liqian Qin , Yuchao Tang , Jigen Peng