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Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…

Optimization and Control · Mathematics 2019-06-28 Jacob H. Seidman , Mahyar Fazlyab , Victor M. Preciado , George J. Pappas

We present a stochastic setting for optimization problems with nonsmooth convex separable objective functions over linear equality constraints. To solve such problems, we propose a stochastic Alternating Direction Method of Multipliers…

Machine Learning · Computer Science 2013-01-23 Hua Ouyang , Niao He , Alexander Gray

In this paper, we propose and analyze an inexact version of the symmetric proximal alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems. Basically, the method allows its first subproblem…

Optimization and Control · Mathematics 2020-06-05 Vando A. Adona , Max L. N. Gonçalves

In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…

Optimization and Control · Mathematics 2023-11-27 Yurii Nesterov

In this note, we show a sublinear nonergodic convergence rate for the algorithm developed in [Bai, et al. Generalized symmetric ADMM for separable convex optimization. Comput. Optim. Appl. 70, 129-170 (2018)], as well as its linear…

Numerical Analysis · Mathematics 2019-06-20 Jianchao Bai , Xiaokai Chang , Jicheng Li , Fengmin Xu

The generalized alternating direction method of multipliers (ADMM) of Xiao et al. [{\tt Math. Prog. Comput., 2018}] aims at the two-block linearly constrained composite convex programming problem, in which each block is in the form of…

Optimization and Control · Mathematics 2022-04-05 Hongwu Li , Haibin Zhang , Yunhai Xiao

The alternating direction method of multipliers (ADMM) has been popular for solving many signal processing problems, convex or nonconvex. In this paper, we study an asynchronous implementation of the ADMM for solving a nonconvex nonsmooth…

Information Theory · Computer Science 2014-12-19 Mingyi Hong

This paper presents a majorized alternating direction method of multipliers (ADMM) with indefinite proximal terms for solving linearly constrained $2$-block convex composite optimization problems with each block in the objective being the…

Optimization and Control · Mathematics 2015-06-24 Min Li , Defeng Sun , Kim-Chuan Toh

We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…

Numerical Analysis · Mathematics 2013-01-10 David I. Ketcheson , Aron J. Ahmadia

Using gradient descent (GD) with fixed or decaying step-size is a standard practice in unconstrained optimization problems. However, when the loss function is only locally convex, such a step-size schedule artificially slows GD down as it…

Machine Learning · Statistics 2023-02-03 Nhat Ho , Tongzheng Ren , Sujay Sanghavi , Purnamrita Sarkar , Rachel Ward

The alternating direction method of multipliers (ADMM) is a flexible method to solve a large class of convex minimization problems. Particular features are its unconditional convergence with respect to the involved step size and its direct…

Numerical Analysis · Mathematics 2017-04-21 Sören Bartels , Marijo Milicevic

Approximate dynamic programming (ADP) has proven itself in a wide range of applications spanning large-scale transportation problems, health care, revenue management, and energy systems. The design of effective ADP algorithms has many…

Optimization and Control · Mathematics 2014-07-15 Ilya O. Ryzhov , Peter I. Frazier , Warren B. Powell

In this paper, we develop a symmetric accelerated stochastic Alternating Direction Method of Multipliers (SAS-ADMM) for solving separable convex optimization problems with linear constraints. The objective function is the sum of a possibly…

Optimization and Control · Mathematics 2021-12-21 Jianchao Bai , Deren Han , Hao Sun , Hongchao Zhang

In this paper, we propose AdaBB, an adaptive gradient method based on the Barzilai-Borwein stepsize. The algorithm is line-search-free and parameter-free, and essentially provides a convergent variant of the Barzilai-Borwein method for…

Optimization and Control · Mathematics 2024-01-17 Danqing Zhou , Shiqian Ma , Junfeng Yang

For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach…

Optimization and Control · Mathematics 2022-12-14 Thang Tran Ngoc , Hai Trinh Ngoc

In this paper, we extend the improved pointwise iteration-complexity result of a dynamic regularized alternating direction method of multipliers (ADMM) for a new stepsize domain. In this complexity analysis, the stepsize parameter can even…

Optimization and Control · Mathematics 2017-05-10 M. L. N. Goncalves

In this paper, we study a general optimization model, which covers a large class of existing models for many applications in imaging sciences. To solve the resulting possibly nonconvex, nonsmooth and non-Lipschitz optimization problem, we…

Optimization and Control · Mathematics 2016-09-30 Lei Yang , Ting Kei Pong , Xiaojun Chen

In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…

Optimization and Control · Mathematics 2020-10-06 Francesco Farina , Giuseppe Notarstefano

We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…

Optimization and Control · Mathematics 2019-04-01 Fatemeh Mansoori , Ermin Wei

Existing asynchronous distributed optimization algorithms often use diminishing step-sizes that cause slow practical convergence, or use fixed step-sizes that depend on and decrease with an upper bound of the delays. Not only are such delay…

Optimization and Control · Mathematics 2024-11-08 Xuyang Wu , Changxin Liu , Sindri Magnusson , Mikael Johansson