Related papers: A First-Order Algorithm for Decentralised Min-Max …
In this paper we consider a distributed optimization scenario in which a set of processors aims at minimizing the maximum of a collection of "separable convex functions" subject to local constraints. This set-up is motivated by peak-demand…
These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…
The paper studies decentralized optimization over networks, where agents minimize a composite objective consisting of the sum of smooth convex functions--the agents' losses--and an additional nonsmooth convex extended value function. We…
In this work, we are concerned with the decentralized optimization problem: \begin{equation*} \min_{x \in \Omega}~f(x) = \frac{1}{n} \sum_{i=1}^n f_i (x), \end{equation*} where $\Omega \subset \mathbb{R}^d$ is a convex domain and each $f_i…
We consider a decentralized convex unconstrained optimization problem, where the cost function can be decomposed into a sum of strongly convex and smooth functions, associated with individual agents, interacting over a static or…
Decentralized optimization methods enable on-device training of machine learning models without a central coordinator. In many scenarios communication between devices is energy demanding and time consuming and forms the bottleneck of the…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
Decentralized optimization algorithms have received much attention due to the recent advances in network information processing. However, conventional decentralized algorithms based on projected gradient descent are incapable of handling…
This work studies multi-agent sharing optimization problems with the objective function being the sum of smooth local functions plus a convex (possibly non-smooth) function coupling all agents. This scenario arises in many machine learning…
In this paper we study convex bi-level optimization problems for which the inner level consists of minimization of the sum of smooth and nonsmooth functions. The outer level aims at minimizing a smooth and strongly convex function over the…
We study non-convex distributed optimization problems where a set of agents collaboratively solve a separable optimization problem that is distributed over a time-varying network. The existing methods to solve these problems rely on (at…
This paper studies decentralized convex-concave minimax optimization problems of the form $\min_x\max_y f(x,y) \triangleq\frac{1}{m}\sum_{i=1}^m f_i(x,y)$, where $m$ is the number of agents and each local function can be written as…
We provide improved convergence rates for constrained convex-concave min-max problems and monotone variational inequalities with higher-order smoothness. In min-max settings where the $p^{th}$-order derivatives are Lipschitz continuous, we…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…
This paper optimizes the step coefficients of first-order methods for smooth convex minimization in terms of the worst-case convergence bound (i.e., efficiency) of the decrease in the gradient norm. This work is based on the performance…
A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…
This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\"older…
We propose a new first-order optimization algorithm -- AcceleratedGradient-OptimisticGradient (AG-OG) Descent Ascent -- for separable convex-concave minimax optimization. The main idea of our algorithm is to carefully leverage the structure…
In this paper, we showcase the interplay between discrete and continuous optimization in network-structured settings. We propose the first fully decentralized optimization method for a wide class of non-convex objective functions that…