English
Related papers

Related papers: Primal-dual fast gradient method with a model

200 papers

This paper investigates accelerating the convergence of distributed optimization algorithms on non-convex problems. We propose a distributed primal-dual stochastic gradient descent~(SGD) equipped with "powerball" method to accelerate. We…

Optimization and Control · Mathematics 2021-10-15 Shengjun Zhang , Colleen P. Bailey

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

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

Classical primal-dual algorithms attempt to solve $\max_{\mu}\min_{x} \mathcal{L}(x,\mu)$ by alternatively minimizing over the primal variable $x$ through primal descent and maximizing the dual variable $\mu$ through dual ascent. However,…

Optimization and Control · Mathematics 2023-11-20 Kaizhao Sun , Andy Sun

We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…

Optimization and Control · Mathematics 2013-02-19 Valentin Nedelcu , Ion Necoara , Quoc Tran Dinh

We study the bilinearly coupled minimax problem: $\min_{x} \max_{y} f(x) + y^\top A x - h(y)$, where $f$ and $h$ are both strongly convex smooth functions and admit first-order gradient oracles. Surprisingly, no known first-order algorithms…

Optimization and Control · Mathematics 2022-01-20 Kiran Koshy Thekumparampil , Niao He , Sewoong Oh

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…

Optimization and Control · Mathematics 2015-03-04 Quoc Tran-Dinh , Volkan Cevher

We propose a primal-dual smoothing framework for finding a near-stationary point of a class of non-smooth non-convex optimization problems with max-structure. We analyze the primal and dual gradient complexities of the framework via two…

Optimization and Control · Mathematics 2023-07-19 Renbo Zhao

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

Numerical Analysis · Mathematics 2025-06-16 Jianchao Bai , Linyuan Jia , Zheng Peng

We propose a novel continuous-time algorithm for inequality-constrained convex optimization inspired by proportional-integral control. Unlike the popular primal-dual gradient dynamics, our method includes a proportional term to control the…

Optimization and Control · Mathematics 2024-09-12 V. Cerone , S. M. Fosson , S. Pirrera , D. Regruto

There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…

Optimization and Control · Mathematics 2024-01-02 Haihao Lu , Jinwen Yang

The primal-dual distributed optimization methods have broad large-scale machine learning applications. Previous primal-dual distributed methods are not applicable when the dual formulation is not available, e.g. the sum-of-non-convex…

Machine Learning · Computer Science 2017-10-30 Zhouyuan Huo , Heng Huang

The problem of constrained Markov decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its utilities/costs. A new primal-dual approach is…

Optimization and Control · Mathematics 2021-10-22 Tianjiao Li , Ziwei Guan , Shaofeng Zou , Tengyu Xu , Yingbin Liang , Guanghui Lan

In this work, we revisit a classical incremental implementation of the primal-descent dual-ascent gradient method used for the solution of equality constrained optimization problems. We provide a short proof that establishes the linear…

Optimization and Control · Mathematics 2020-01-17 Sulaiman A. Alghunaim , Ali H. Sayed

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

We study a class of optimization problems in which the objective function is given by the sum of a differentiable but possibly nonconvex component and a nondifferentiable convex regularization term. We introduce an auxiliary variable to…

Optimization and Control · Mathematics 2019-08-27 Neil K. Dhingra , Sei Zhen Khong , Mihailo R. Jovanović

In this paper we investigate the convergence of a recently popular class of first-order primal-dual algorithms for saddle point problems under the presence of errors occurring in the proximal maps and gradients. We study several types of…

Optimization and Control · Mathematics 2020-02-26 Julian Rasch , Antonin Chambolle

In this paper, we propose a primal-dual algorithm with a novel momentum term using the partial gradients of the coupling function that can be viewed as a generalization of the method proposed by Chambolle and Pock in 2016 to solve saddle…

Optimization and Control · Mathematics 2020-10-22 Erfan Yazdandoost Hamedani , Necdet Serhat Aybat

Motivated by an inertial primal-dual dynamical system with vanishing damping, we propose a class of accelerated augmented Lagrangian methods with Nesterov extrapolation parameters for a linearly constrained convex optimization problem with…

Optimization and Control · Mathematics 2026-05-28 Xin He , Nan-Jing Huang , Yi-Bin Xiao , Ya-Ping Fang

This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…

Optimization and Control · Mathematics 2021-11-23 Kui Zhu , Yutao Tang