Related papers: A novel interpretation of Nesterov's acceleration …
This paper investigates the point convergence of accelerated gradient methods for multiobjective optimization, in both continuous and discrete settings. We address the open problems of whether the solution trajectory of the multiobjective…
In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of…
We propose a class of \textit{Euler-Lagrange} equations indexed by a pair of parameters ($\alpha,r$) that generalizes Nesterov's accelerated gradient methods for convex ($\alpha=1$) and strongly convex ($\alpha=0$) functions from a…
The high-resolution differential equation framework has been proven to be tailor-made for Nesterov's accelerated gradient descent method~(\texttt{NAG}) and its proximal correspondence -- the class of faster iterative shrinkage thresholding…
We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the…
We study convex optimization problems over a compact convex set where projections are expensive but a linear minimization oracle (LMO) is available. We propose the adaptive conditional gradient sliding method (AdCGS), a projection-free and…
We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…
Nesterov's accelerated gradient method for minimizing a smooth strongly convex function $f$ is known to reduce $f(\x_k)-f(\x^*)$ by a factor of $\eps\in(0,1)$ after $k\ge O(\sqrt{L/\ell}\log(1/\eps))$ iterations, where $\ell,L$ are the two…
While Nesterov's Accelerated Gradient Descent (AGD) efficiently solves constrained problems when the constraint set $X \subseteq \mathbb{R}^n$ is simple and easy to project onto, it remains an open question whether function-constrained…
Gradient restarting has been shown to improve the numerical performance of accelerated gradient methods. This paper provides a mathematical analysis to understand these advantages. First, we establish global linear convergence guarantees…
We introduce a generic scheme for accelerating gradient-based optimization methods in the sense of Nesterov. The approach, called Catalyst, builds upon the inexact accelerated proximal point algorithm for minimizing a convex objective…
Nesterov SGD is widely used for training modern neural networks and other machine learning models. Yet, its advantages over SGD have not been theoretically clarified. Indeed, as we show in our paper, both theoretically and empirically,…
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…
We consider gradient descent with `momentum', a widely used method for loss function minimization in machine learning. This method is often used with `Nesterov acceleration', meaning that the gradient is evaluated not at the current…
We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical…
We present a variant of accelerated gradient descent algorithms, adapted from Nesterov's optimal first-order methods, for weakly-quasi-convex and weakly-quasi-strongly-convex functions. We show that by tweaking the so-called estimate…
Accelerated gradient methods like Nesterov's Accelerated Gradient (NAG) achieve faster convergence on well-conditioned problems but often diverge on ill-conditioned or non-convex landscapes due to aggressive momentum accumulation. We…
Nesterov's accelerated gradient descent (AGD), an instance of the general family of "momentum methods", provably achieves faster convergence rate than gradient descent (GD) in the convex setting. However, whether these methods are superior…
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…
We consider the problem of minimizing a strongly convex smooth function where the gradients are subject to additive worst-case deterministic errors that are square-summable. We study the trade-offs between the convergence rate and…