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We propose a family of optimization methods that achieve linear convergence using first-order gradient information and constant step sizes on a class of convex functions much larger than the smooth and strongly convex ones. This larger…

Optimization and Control · Mathematics 2018-09-14 Chris J. Maddison , Daniel Paulin , Yee Whye Teh , Brendan O'Donoghue , Arnaud Doucet

We propose a first-order method for stochastic strongly convex optimization that attains $O(1/n)$ rate of convergence, analysis show that the proposed method is simple, easily to implement, and in worst case, asymptotically four times…

Optimization and Control · Mathematics 2011-10-14 Peng Cheng

This paper considers decentralized consensus optimization problems where different summands of a global objective function are available at nodes of a network that can communicate with neighbors only. The proximal method of multipliers is…

Optimization and Control · Mathematics 2016-02-02 Aryan Mokhtari , Wei Shi , Qing Ling , Alejandro Ribeiro

In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal…

Optimization and Control · Mathematics 2014-02-04 Ion Necoara , Valentin Nedelcu

We present in this paper first-order alternating linearization algorithms based on an alternating direction augmented Lagrangian approach for minimizing the sum of two convex functions. Our basic methods require at most $O(1/\epsilon)$…

Optimization and Control · Mathematics 2010-10-14 Donald Goldfarb , Shiqian Ma , Katya Scheinberg

We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function,…

Optimization and Control · Mathematics 2015-06-12 Euhanna Ghadimi , Iman Shames , Mikael Johansson

We present a family of algorithms, called descent algorithms, for optimizing convex and non-convex functions. We also introduce a new first-order algorithm, called rescaled gradient descent (RGD), and show that RGD achieves a faster…

Optimization and Control · Mathematics 2020-01-07 Ashia Wilson , Lester Mackey , Andre Wibisono

Motivated by applications to distributed optimization over networks and large-scale data processing in machine learning, we analyze the deterministic incremental aggregated gradient method for minimizing a finite sum of smooth functions…

Optimization and Control · Mathematics 2018-01-16 Mert Gurbuzbalaban , Asuman Ozdaglar , Pablo Parrilo

In convex optimization, there is an {\em acceleration} phenomenon in which we can boost the convergence rate of certain gradient-based algorithms. We can observe this phenomenon in Nesterov's accelerated gradient descent, accelerated mirror…

Optimization and Control · Mathematics 2015-09-14 Andre Wibisono , Ashia C. Wilson

This paper delves into the investigation of a distributed aggregative optimization problem within a network. In this scenario, each agent possesses its own local cost function, which relies not only on the local state variable but also on…

Optimization and Control · Mathematics 2025-04-01 Jiaxu Liu , Song Chen , Shengze Cai , Chao Xu , Jian Chu

In this paper, we generalize proximal methods that were originally designed for convex optimization on normed vector space to non-convex pose graph optimization (PGO) on special Euclidean groups, and show that our proposed generalized…

Optimization and Control · Mathematics 2021-05-05 Taosha Fan , Todd Murphey

This paper considers the distributed optimization problem over a network, where the objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. We develop an Accelerated…

Optimization and Control · Mathematics 2020-06-02 Guannan Qu , Na Li

We investigate a distributed optimization problem over a cooperative multi-agent time-varying network, where each agent has its own decision variables that should be set so as to minimize its individual objective subject to local…

Optimization and Control · Mathematics 2018-05-24 Chuanye Gu , Zhiyou Wu , Jueyou Li

This work establishes new convergence guarantees for gradient descent in smooth convex optimization via a computer-assisted analysis technique. Our theory allows nonconstant stepsize policies with frequent long steps potentially violating…

Optimization and Control · Mathematics 2024-02-06 Benjamin Grimmer

The incremental aggregated gradient algorithm is popular in network optimization and machine learning research. However, the current convergence results require the objective function to be strongly convex. And the existing convergence…

Optimization and Control · Mathematics 2019-10-14 Tao Sun , Yuejiao Sun , Dongsheng Li , Qing Liao

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

We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…

Numerical Analysis · Mathematics 2021-07-28 J. J. Alvarez-Sanchez , M. Gadella , L. P. Lara

It is well known that both gradient descent and stochastic coordinate descent achieve a global convergence rate of $O(1/k)$ in the objective value, when applied to a scheme for minimizing a Lipschitz-continuously differentiable,…

Optimization and Control · Mathematics 2019-05-15 Ching-pei Lee , Stephen J. Wright

We consider a class of popular distributed non-convex optimization problems, in which agents connected by a network $\mathcal{G}$ collectively optimize a sum of smooth (possibly non-convex) local objective functions. We address the…

Optimization and Control · Mathematics 2020-01-08 Haoran Sun , Mingyi Hong

We consider distributed optimization in random networks where N nodes cooperatively minimize the sum \sum_{i=1}^N f_i(x) of their individual convex costs. Existing literature proposes distributed gradient-like methods that are…

Information Theory · Computer Science 2023-07-19 Dusan Jakovetic , Joao Xavier , Jose M. F. Moura