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Linear constrained convex programming has many practical applications, including support vector machine and machine learning portfolio problems. We propose the randomized primal-dual coordinate (RPDC) method, a randomized coordinate…

Optimization and Control · Mathematics 2020-09-01 Daoli Zhu , Lei Zhao

We propose a new image restoration model based on the minimized surface regularization. The proposed model closely relates to the classical smoothing ROF model \cite{4}. We can reformulate the proposed model as a min-max problem and solve…

Optimization and Control · Mathematics 2016-05-31 Zhi-Feng Pang , Yuping Duan

We consider minimizing the sum of three convex functions, where the first one F is smooth, the second one is nonsmooth and proximable and the third one is the composition of a nonsmooth proximable function with a linear operator L. This…

Optimization and Control · Mathematics 2022-07-27 Adil Salim , Laurent Condat , Konstantin Mishchenko , Peter Richtárik

We study the non-smooth optimization problems in machine learning, where both the loss function and the regularizer are non-smooth functions. Previous studies on efficient empirical loss minimization assume either a smooth loss function or…

Machine Learning · Computer Science 2013-07-29 Tianbao Yang , Mehrdad Mahdavi , Rong Jin , Shenghuo Zhu

In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…

Optimization and Control · Mathematics 2023-05-09 Jie Liu , Xiaoqing Ou , Jiawei Chen

We introduce a primal-dual stochastic gradient oracle method for distributed convex optimization problems over networks. We show that the proposed method is optimal in terms of communication steps. Additionally, we propose a new analysis…

Optimization and Control · Mathematics 2019-11-28 Darina Dvinskikh , Eduard Gorbunov , Alexander Gasnikov , Pavel Dvurechensky , Cesar A. Uribe

We present a primal-dual majorization-minimization method for solving large-scale linear programs. A smooth barrier augmented Lagrangian (SBAL) function with strict convexity for the dual linear program is derived. The…

Optimization and Control · Mathematics 2022-08-09 Xin-Wei Liu , Yu-Hong Dai , Ya-Kui Huang

Entropy regularized Markov decision processes have been widely used in reinforcement learning. This paper is concerned with the primal-dual formulation of the entropy regularized problems. Standard first-order methods suffer from slow…

Optimization and Control · Mathematics 2023-06-13 Haoya Li , Hsiang-fu Yu , Lexing Ying , Inderjit Dhillon

Based on a preconditioned version of the randomized block-coordinate forward-backward algorithm recently proposed in [Combettes,Pesquet,2014], several variants of block-coordinate primal-dual algorithms are designed in order to solve a wide…

Optimization and Control · Mathematics 2014-10-28 Jean-Christophe Pesquet , Audrey Repetti

We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex…

Optimization and Control · Mathematics 2017-01-23 Loris Cannelli , Francisco Facchinei , Vyacheslav Kungurtsev , Gesualdo Scutari

We consider stochastic convex optimization problems with affine constraints and develop several methods using either primal or dual approach to solve it. In the primal case, we use a special penalization technique to make the initial…

Optimization and Control · Mathematics 2020-11-13 Eduard Gorbunov , Darina Dvinskikh , Alexander Gasnikov

This article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the…

Optimization and Control · Mathematics 2025-03-14 Zixuan Liu , Xuyang Wu , Dandan Wang , Jie Lu

This paper considers convex optimization problems where nodes of a network have access to summands of a global objective. Each of these local objectives is further assumed to be an average of a finite set of functions. The motivation for…

Optimization and Control · Mathematics 2015-06-16 Aryan Mokhtari , Alejandro Ribeiro

We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum $\sum_{i=1}^{m}f_i(z)$ of functions over in a network. We provide complexity bounds for four different…

Optimization and Control · Mathematics 2020-03-17 César A. Uribe , Soomin Lee , Alexander Gasnikov , Angelia Nedić

Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…

Optimization and Control · Mathematics 2019-08-30 Yu-Chao Tang , Chuan-Xi Zhu , Meng Wen , Ji-Gen Peng

We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this…

Optimization and Control · Mathematics 2021-04-13 Renbo Zhao

This paper deals with the analysis of a recent reformulation of the primal-dual hybrid gradient method [Zhu and Chan 2008, Pock, Cremers, Bischof and Chambolle 2009, Esser, Zhang and Chan 2010, Chambolle and Pock 2011], which allows to…

Numerical Analysis · Mathematics 2014-07-08 Thomas Möllenhoff , Evgeny Strekalovskiy , Michael Moeller , Daniel Cremers

We consider stochastic strongly-convex-strongly-concave (SCSC) saddle point (SP) problems which frequently arise in applications ranging from distributionally robust learning to game theory and fairness in machine learning. We focus on the…

Optimization and Control · Mathematics 2023-07-17 Yassine Laguel , Necdet Serhat Aybat , Mert Gürbüzbalaban

Empirically it has been observed that the performance of deep neural networks steadily improves as we increase model size, contradicting the classical view on overfitting and generalization. Recently, the double descent phenomena has been…

Machine Learning · Computer Science 2021-07-28 Ilja Kuzborskij , Csaba Szepesvári , Omar Rivasplata , Amal Rannen-Triki , Razvan Pascanu

Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…

Optimization and Control · Mathematics 2024-01-17 Xiaokai Chang , Junfeng Yang , Hongchao Zhang