Related papers: Generalized Continuous-Time Models for Nesterov's …
Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…
The generalized perturbative approach is an all purpose variant of Stein's method used to obtain rates of normal approximation. Originally developed for functions of independent random variables this method is here extended to functions of…
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…
This paper considers the problem of understanding the behavior of a general class of accelerated gradient methods on smooth nonconvex functions. Motivated by some recent works that have proposed effective algorithms, based on Polyak's heavy…
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 distributed optimization problems when $N$ nodes minimize the sum of their individual costs subject to a common vector variable. The costs are convex, have Lipschitz continuous gradient (with constant $L$), and bounded gradient. We…
We formulate two classes of first-order algorithms more general than previously studied for minimizing smooth and strongly convex or, respectively, smooth and convex functions. We establish sufficient conditions, via new discrete Lyapunov…
First-order methods play a central role in large-scale machine learning. Even though many variations exist, each suited to a particular problem, almost all such methods fundamentally rely on two types of algorithmic steps: gradient descent,…
We study the problem of characterizing the expected hitting times for a robust generalization of continuous-time Markov chains. This generalization is based on the theory of imprecise probabilities, and the models with which we work…
We propose a new framework to design and analyze accelerated methods that solve general monotone equation (ME) problems $F(x)=0$. Traditional approaches include generalized steepest descent methods and inexact Newton-type methods. If $F$ is…
This paper is devoted to the study of accelerated proximal gradient methods where the sequence that controls the momentum term doesn't follow Nesterov's rule. We propose a relaxed weak accelerated proximal gradient (R-WAPG) method, a…
We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…
While momentum-based optimization algorithms are commonly used in the notoriously non-convex optimization problems of deep learning, their analysis has historically been restricted to the convex and strongly convex setting. In this article,…
In this paper, we propose Nesterov Accelerated Shuffling Gradient (NASG), a new algorithm for the convex finite-sum minimization problems. Our method integrates the traditional Nesterov's acceleration momentum with different shuffling…
Momentum methods, including heavy-ball~(HB) and Nesterov's accelerated gradient~(NAG), are widely used in training neural networks for their fast convergence. However, there is a lack of theoretical guarantees for their convergence and…
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…
In this paper, we consider Nesterov's Accelerated Gradient method for solving Nonlinear Inverse and Ill-Posed Problems. Known to be a fast gradient-based iterative method for solving well-posed convex optimization problems, this method also…
Over the past two decades, descent methods have received substantial attention within the multiobjective optimization field. Nonetheless, both theoretical analyses and empirical evidence reveal that existing first-order methods for…
In a Hilbert framework, for convex differentiable optimization, we consider accelerated gradient methods obtained by combining temporal scaling and averaging techniques with Tikhonov regularization. We start from the continuous steepest…
We develop the theory of discrete-time gradient flows for convex functions on Alexandrov spaces with arbitrary upper or lower curvature bounds. We employ different resolvent maps in the upper and lower curvature bound cases to construct…