Related papers: A novel interpretation of Nesterov's acceleration …

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…

Variance reduction is a crucial tool for improving the slow convergence of stochastic gradient descent. Only a few variance-reduced methods, however, have yet been shown to directly benefit from Nesterov's acceleration techniques to match…

Nesterov's accelerated gradient (AG) method for minimizing a smooth strongly convex function $f$ is known to reduce $f({\bf x}_k)-f({\bf x}^*)$ by a factor of $\epsilon\in(0,1)$ after $k=O(\sqrt{L/\ell}\log(1/\epsilon))$ iterations, where…

Randomized-subspace methods reduce the cost of first-order optimization by using only low-dimensional projected-gradient information, a feature that is attractive in forward-mode automatic differentiation and communication-limited settings.…

This work proposes a novel adaptive linearized alternating direction multiplier method (LADMM) to convex optimization, which improves the convergence rate of the LADMM-based algorithm by adjusting step-size iteratively.The innovation of…

Multinomial logistic regression, also known by other names such as multiclass logistic regression and softmax regression, is a fundamental classification method that generalizes binary logistic regression to multiclass problems. A recently…

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…

Motivated by the fact that the gradient-based optimization algorithms can be studied from the perspective of limiting ordinary differential equations (ODEs), here we derive an ODE representation of the accelerated triple momentum (TM)…

Based on SGD, previous works have proposed many algorithms that have improved convergence speed and generalization in stochastic optimization, such as SGDm, AdaGrad, Adam, etc. However, their convergence analysis under non-convex conditions…

We present a unified convergence analysis for first order convex optimization methods using the concept of strong Lyapunov conditions. Combining this with suitable time scaling factors, we are able to handle both convex and strong convex…

A longstanding challenge in optimization is achieving optimal performance when the strong convexity parameter m is unknown. In this paper, we propose NAG-free, a simple extension of Nesterov's accelerated gradient (NAG) which is the first…

Empirically, it has been observed that adding momentum to Stochastic Gradient Descent (SGD) accelerates the convergence of the algorithm. However, the literature has been rather pessimistic, even in the case of convex functions, about the…

In this paper, we focus on the problem of minimizing a continuously differentiable convex objective function, $\min_x f(x)$. Recently, Malitsky (2020); Alacaoglu et al.(2023) developed an adaptive first-order method, GRAAL. This algorithm…

We propose AdaNAG, an adaptive accelerated gradient method based on Nesterov's accelerated gradient method. AdaNAG is line-search-free, parameter-free, and achieves the accelerated convergence rates $f(x_k) - f_\star =…

We study nonsmooth convex minimization through a continuous-time dynamical system that can be seen as a high-resolution ODE of Nesterov Accelerated Gradient (NAG) adapted to the nonsmooth case. We apply a time-varying Moreau envelope…

Convergence analysis of Nesterov's accelerated gradient method has attracted significant attention over the past decades. While extensive work has explored its theoretical properties and elucidated the intuition behind its acceleration, a…

We consider problems of minimizing functionals $\mathcal{F}$ of probability measures on the Euclidean space. To propose an accelerated gradient descent algorithm for such problems, we consider gradient flow of transport maps that give…

In this work, based on the continuous time approach, we propose an accelerated gradient method with adaptive residual restart for convex multiobjective optimization problems. For the first, we derive rigorously the continuous limit of the…

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…

This paper is concerned with temporal convergence analysis of the recently introduced Dynamically Regularized Lagrange Multiplier (DRLM) method for the incompressible Navier-Stokes equations. A key feature of the DRLM approach is the…