English
Related papers

Related papers: Toward Designing Convergent Deep Operator Splittin…

200 papers

Classifiers are biased when trained on biased datasets. As a remedy, we propose Learning to Split (ls), an algorithm for automatic bias detection. Given a dataset with input-label pairs, ls learns to split this dataset so that predictors…

Machine Learning · Computer Science 2022-07-22 Yujia Bao , Regina Barzilay

Convex-nonconvex (CNC) regularization is a novel paradigm that employs a nonconvex penalty function while maintaining the convexity of the entire objective function. It has been successfully applied to problems in signal processing,…

Optimization and Control · Mathematics 2025-02-21 Qiang Heng , Xiaoqian Liu , Eric C. Chi

Consider the problem of minimizing the sum of two convex functions, one being smooth and the other non-smooth. In this paper, we introduce a general class of approximate proximal splitting (APS) methods for solving such minimization…

Optimization and Control · Mathematics 2014-04-23 Mojtaba Kadkhodaie , Maziar Sanjabi , Zhi-Quan Luo

We consider the problem of estimating the inverse covariance matrix by maximizing the likelihood function with a penalty added to encourage the sparsity of the resulting matrix. We propose a new approach based on the split Bregman method to…

Machine Learning · Statistics 2015-03-17 Gui-Bo Ye , Jian-Feng Cai , Xiaohui Xie

In this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic…

Optimization and Control · Mathematics 2018-08-23 Deming Yuan , Yiguang Hong , Daniel W. C. Ho , Guoping Jiang

In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…

Numerical Analysis · Mathematics 2020-08-20 Yalchin Efendiev , Petr N. Vabishchevich

Operator splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which all simple pieces of the…

Optimization and Control · Mathematics 2015-07-09 Damek Davis

The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…

Optimization and Control · Mathematics 2019-08-30 Yu-Chao Tang , Guo-Rong Wu , Chuan-Xi Zhu

We consider the problem of covariance matrix estimation in the presence of latent variables. Under suitable conditions, it is possible to learn the marginal covariance matrix of the observed variables via a tractable convex program, where…

Machine Learning · Statistics 2011-10-17 Gui-Bo Ye , Yuanfeng Wang , Yifei Chen , Xiaohui Xie

We introduce a novel approach addressing global analysis of a difficult class of nonconvex-nonsmooth optimization problems within the important framework of Lagrangian-based methods. This genuine nonlinear class captures many problems in…

Optimization and Control · Mathematics 2018-01-10 Jérôme Bolte , Shoham Sabach , Marc Teboulle

The training of deep neural networks predominantly relies on a combination of gradient-based optimisation and back-propagation for the computation of the gradient. While incredibly successful, this approach faces challenges such as…

Machine Learning · Computer Science 2026-02-09 Xiaoyu Wang , Alexandra Valavanis , Azhir Mahmood , Andreas Mang , Martin Benning , Audrey Repetti

We introduce new planning and reinforcement learning algorithms for discounted MDPs that utilize an approximate model of the environment to accelerate the convergence of the value function. Inspired by the splitting approach in numerical…

Machine Learning · Computer Science 2022-11-28 Amin Rakhsha , Andrew Wang , Mohammad Ghavamzadeh , Amir-massoud Farahmand

We study a stochastic and distributed algorithm for nonconvex problems whose objective consists of a sum of $N$ nonconvex $L_i/N$-smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm…

Optimization and Control · Mathematics 2017-06-06 Davood Hajinezhad , Mingyi Hong , Tuo Zhao , Zhaoran Wang

Although the performance of popular optimization algorithms such as Douglas-Rachford splitting (DRS) and the ADMM is satisfactory in small and well-scaled problems, ill conditioning and problem size pose a severe obstacle to their reliable…

Optimization and Control · Mathematics 2024-04-17 Andreas Themelis , Lorenzo Stella , Panagiotis Patrinos

Non-convex optimization problems are pervasive across mathematical programming, engineering design, and scientific computing, often posing intractable challenges for traditional solvers due to their complex objective functions and…

Computation and Language · Computer Science 2026-01-09 Xinyue Peng , Yanming Liu , Yihan Cang , Yuwei Zhang , Xinyi Wang , Songhang Deng , Jiannan Cao

The impressive performance of Large Language Models (LLMs) across various natural language processing tasks comes at the cost of vast computational resources and storage requirements. One-shot pruning techniques offer a way to alleviate…

Machine Learning · Computer Science 2025-09-09 Xiang Meng , Kayhan Behdin , Haoyue Wang , Rahul Mazumder

The three operator splitting scheme was recently proposed by [Davis and Yin, 2015] as a method to optimize composite objective functions with one convex smooth term and two convex (possibly non-smooth) terms for which we have access to…

Machine Learning · Statistics 2021-06-29 Fabian Pedregosa

Large-scale unconstrained optimization is a fundamental and important class of, yet not well-solved problems in numerical optimization. The main challenge in designing an algorithm is to require a few storage locations or very inexpensive…

Optimization and Control · Mathematics 2020-01-24 Zheng Li , Shi Shu , Jian-Ping Zhang

In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…

Optimization and Control · Mathematics 2018-12-20 Mario Souto , Joaquim D. Garcia , Alvaro Veiga

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