6 papers
The Iterates of Nesterov's Accelerated Algorithm Converge in The Critical Regimes
Radu Ioan Bot, Jalal Fadili, Dang-Khoa Nguyen
In this paper, we prove that the iterates of the accelerated Nesterov's algorithm in the critical regime do converge in the weak topology to a global minimizer of an -smooth fun…
Fast Reflected Forward-Backward algorithm: achieving fast convergence rates for convex optimization with linear cone constraints
Radu Ioan Bot, Dang-Khoa Nguyen, Chunxiang Zong
In this paper, we derive a Fast Reflected Forward-Backward (Fast RFB) algorithm to solve the problem of finding a zero of the sum of a maximally monotone operator and a monotone an…
Tikhonov regularization of monotone operator flows not only ensures strong convergence of the trajectories but also speeds up the vanishing of the residuals
Radu Ioan Bot, Dang-Khoa Nguyen
In the framework of real Hilbert spaces, we investigate first-order dynamical systems governed by monotone and continuous operators. We demonstrate that when the monotone operator…
Recovering Nesterov accelerated dynamics from Heavy Ball dynamics via time rescaling
Hedy Attouch, Radu Ioan Bot, David Alexander Hulett +1
In a real Hilbert space, we consider two classical problems: the global minimization of a smooth and convex function (i.e., a convex optimization problem) and finding the zeros…
Fast convex optimization via closed-loop time scaling of gradient dynamics
Hedy Attouch, Radu Ioan Bot, Dang-Khoa Nguyen
In a Hilbert setting, for convex differentiable optimization, we develop a general framework for adaptive accelerated gradient methods. They are based on damped inertial dynamics w…
Fast second-order dynamics with slow vanishing damping approaching the zeros of a monotone and continuous operator
Radu Ioan Bot, David Alexander Hulett, Dang-Khoa Nguyen
In this work, we approach the problem of finding the zeros of a continuous and monotone operator through a second-order dynamical system with a damping term of the form ,…