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Related papers: Optimal Algorithms for Non-Smooth Distributed Opti…

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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

In many important machine learning applications, the standard assumption of having a globally Lipschitz continuous gradient may fail to hold. This paper delves into a more general $(L_0, L_1)$-smoothness setting, which gains particular…

Optimization and Control · Mathematics 2025-02-07 Chenghan Xie , Chenxi Li , Chuwen Zhang , Qi Deng , Dongdong Ge , Yinyu Ye

This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…

Optimization and Control · Mathematics 2020-07-15 Jineng Ren , Jarvis Haupt

We investigate the finite-time analysis of finding ($\delta,\epsilon$)-stationary points for nonsmooth nonconvex objectives in decentralized stochastic optimization. A set of agents aim at minimizing a global function using only their local…

Optimization and Control · Mathematics 2024-06-04 Emre Sahinoglu , Shahin Shahrampour

We develop a distributed stochastic gradient descent algorithm for solving non-convex optimization problems under the assumption that the local objective functions are twice continuously differentiable with Lipschitz continuous gradients…

Optimization and Control · Mathematics 2019-08-20 Jemin George , Tao Yang , He Bai , Prudhvi Gurram

We propose a distributed algorithm based on Alternating Direction Method of Multipliers (ADMM) to minimize the sum of locally known convex functions using communication over a network. This optimization problem emerges in many applications…

Optimization and Control · Mathematics 2016-01-05 Ali Makhdoumi , Asuman Ozdaglar

A lot of effort has been invested into characterizing the convergence rates of gradient based algorithms for non-linear convex optimization. Recently, motivated by large datasets and problems in machine learning, the interest has shifted…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-07-23 Konstantinos I. Tsianos , Michael G. Rabbat

This paper deals with composite optimization problems having the objective function formed as the sum of two terms, one has Lipschitz continuous gradient along random subspaces and may be nonconvex and the second term is simple and…

Optimization and Control · Mathematics 2024-01-10 I. Necoara , F. Chorobura

In this paper we consider a distributed optimization scenario in which the aggregate objective function to minimize is partitioned, big-data and possibly non-convex. Specifically, we focus on a set-up in which the dimension of the decision…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-03-27 Ivano Notarnicola , Giuseppe Notarstefano

In this paper, we present several new results on minimizing a nonsmooth and nonconvex function under a Lipschitz condition. Recent work shows that while the classical notion of Clarke stationarity is computationally intractable up to some…

Optimization and Control · Mathematics 2022-11-08 Michael I. Jordan , Tianyi Lin , Manolis Zampetakis

In stochastic convex optimization problems, most existing adaptive methods rely on prior knowledge about the diameter bound $D$ when the smoothness or the Lipschitz constant is unknown. This often significantly affects performance as only a…

Optimization and Control · Mathematics 2025-10-08 Clément Lezane , Alexandre d'Aspremont

In this paper, we consider distributed optimization problems where the goal is to minimize a sum of objective functions over a multi-agent network. We focus on the case when the inter-agent communication is described by a…

Optimization and Control · Mathematics 2018-06-08 Chenguang Xi , Ran Xin , Usman A. Khan

In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…

Optimization and Control · Mathematics 2020-02-19 Sebastian Banert , Axel Ringh , Jonas Adler , Johan Karlsson , Ozan Öktem

We consider the problem of minimizing the sum of non-smooth convex functions in non-Euclidean spaces, e.g., probability simplex, via only local computation and communication on an undirected graph. We propose two algorithms motivated by…

Optimization and Control · Mathematics 2019-08-22 Yue Yu , Behçet Açıkmeşe , Mehran Mesbahi

We study the oracle complexity of nonsmooth nonconvex optimization, with the algorithm assumed to have access only to local function information. It has been shown by Davis, Drusvyatskiy, and Jiang (2023) that for nonsmooth Lipschitz…

Optimization and Control · Mathematics 2024-09-17 Guy Kornowski , Swati Padmanabhan , Ohad Shamir

This paper considers the distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of local cost functions by using local information exchange. We first consider a distributed first-order primal-dual…

Optimization and Control · Mathematics 2021-08-26 Xinlei Yi , Shengjun Zhang , Tao Yang , Tianyou Chai , Karl H. Johansson

Decentralized optimization has become a fundamental tool for large-scale learning systems; however, most existing methods rely on the classical Lipschitz smoothness assumption, which is often violated in problems with rapidly varying…

Optimization and Control · Mathematics 2026-01-08 Yanan Bo , Yongqiang Wang

We study the problem of distributed zero-order optimization for a class of strongly convex functions. They are formed by the average of local objectives, associated to different nodes in a prescribed network of connections. We propose a…

Optimization and Control · Mathematics 2021-06-29 Arya Akhavan , Massimiliano Pontil , Alexandre B. Tsybakov

We propose a new primal-dual homotopy smoothing algorithm for a linearly constrained convex program, where neither the primal nor the dual function has to be smooth or strongly convex. The best known iteration complexity solving such a…

Optimization and Control · Mathematics 2018-10-25 Xiaohan Wei , Hao Yu , Qing Ling , Michael J. Neely

This paper considers nonconvex distributed constrained optimization over networks, modeled as directed (possibly time-varying) graphs. We introduce the first algorithmic framework for the minimization of the sum of a smooth nonconvex…

Optimization and Control · Mathematics 2018-09-05 Gesualdo Scutari , Ying Sun