相关论文: Convergence Rate Analysis of Accelerated Forward-B…

We study Nesterov's accelerated gradient method with constant step-size and momentum parameters in the stochastic approximation setting (unbiased gradients with bounded variance) and the finite-sum setting (where randomness is due to…

In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…

The Nonlinear Forward-Backward (NFB) algorithm, also known as warped resolvent iterations, is a splitting method for finding zeros of sums of monotone operators. In particular cases, NFB reduces to well-known algorithms such as…

We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing…

High order momentum-based parameter update algorithms have seen widespread applications in training machine learning models. Recently, connections with variational approaches have led to the derivation of new learning algorithms with…

We derive an equivalent form of Halpern's fixed-point iteration scheme for solving a co-coercive equation (also called a root-finding problem), which can be viewed as a Nesterov's accelerated interpretation. We show that one method is…

We develop a distributed algorithm for convex Empirical Risk Minimization, the problem of minimizing large but finite sum of convex functions over networks. The proposed algorithm is derived from directly discretizing the second-order…

We investigate two inertial forward-backward algorithms in connection with the minimization of the sum of a non-smooth and possibly non-convex and a non-convex differentiable function. The algorithms are formulated in the spirit of the…

In a real Hilbert space, we consider two classical problems: the global minimization of a smooth and convex function $f$ (i.e., a convex optimization problem) and finding the zeros of a monotone and continuous operator $V$ (i.e., a monotone…

We present a unifying framework for adapting the update direction in gradient-based iterative optimization methods. As natural special cases we re-derive classical momentum and Nesterov's accelerated gradient method, lending a new intuitive…

Asynchronous algorithms have attracted much attention recently due to the crucial demands on solving large-scale optimization problems. However, the accelerated versions of asynchronous algorithms are rarely studied. In this paper, we…

Convergence analysis of accelerated first-order methods for convex optimization problems are presented from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient flow, has…

Various distributed gradient descent algorithms for multi-agent optimization have incorporated the Nesterov accelerated gradient method, where the use of momentum enhances convergence rates. These algorithms have found broad applications in…

The Krasnosel'skii-Mann (KM) algorithm is the most fundamental iterative scheme designed to find a fixed point of an averaged operator in the framework of a real Hilbert space, since it lies at the heart of various numerical algorithms for…

RMSProp and ADAM continue to be extremely popular algorithms for training neural nets but their theoretical convergence properties have remained unclear. Further, recent work has seemed to suggest that these algorithms have worse…

Deterministic approaches using iterative optimisation have been historically successful in diffeomorphic image registration (DiffIR). Although these approaches are highly accurate, they typically carry a significant computational burden.…

The Alternating Minimization Algorithm (AMA) has been proposed by Tseng to solve convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the latter is assumed to be…

We formulate an affine invariant implementation of the accelerated first-order algorithm in Nesterov (1983). Its complexity bound is proportional to an affine invariant regularity constant defined with respect to the Minkowski gauge of the…

Recently, the anchor acceleration, an acceleration mechanism distinct from Nesterov's, has been discovered for minimax optimization and fixed-point problems, but its mechanism is not understood well, much less so than Nesterov acceleration.…

We study the generalized forward-reflected-backward (GFRB) method, an extension of the forward-reflected-backward (FRB) scheme due to Malitsky and Tam, for solving monotone inclusion problems in real Hilbert spaces. We first analyze GFRB…