3 citations · 4 across the 15 of their papers we have counts for
18 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…
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 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…
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 ,…
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…
Fast Forward-Backward splitting for monotone inclusions with a convergence rate of the tangent residual of
Radu Ioan Bot, Dang-Khoa Nguyen, Chunxiang Zong
We address the problem of finding the zeros of the sum of a maximally monotone operator and a cocoercive operator. Our approach introduces a modification to the forward-backward me…
A Fast Optimistic Method for Monotone Variational Inequalities
Michael Sedlmayer, Dang-Khoa Nguyen, Radu Ioan Bot
We study monotone variational inequalities that can arise as optimality conditions for constrained convex optimisation or convex-concave minimax problems and propose a novel algori…
Accelerated Griffin-Lim algorithm: A fast and provably converging numerical method for phase retrieval
Rossen Nenov, Dang-Khoa Nguyen, Peter Balazs +1
The recovery of a signal from the magnitudes of its transformation, like the Fourier transform, is known as the phase retrieval problem and is of big relevance in various fields of…
Faster than Fast: Accelerating the Griffin-Lim Algorithm
Rossen Nenov, Dang-Khoa Nguyen, Peter Balazs
The phase retrieval problem is found in various areas of applications of engineering and applied physics. It is also a very active field of research in mathematics, signal processi…
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…
Time rescaling of a primal-dual dynamical system with asymptotically vanishing damping
David Alexander Hulett, Dang-Khoa Nguyen
In this work, we approach the minimization of a continuously differentiable convex function under linear equality constraints by a second-order dynamical system with an asymptotica…
Fast convex optimization via time scale and averaging of the steepest descent
Hedy Attouch, Radu Ioan Bot, Dang-Khoa Nguyen
In a Hilbert setting, we develop a gradient-based dynamic approach for fast solving convex optimization problems. By applying time scaling, averaging, and perturbation techniques t…
Fast Krasnosel'skii-Mann algorithm with a convergence rate of the fixed point iteration of
Radu Ioan Bot, Dang-Khoa Nguyen
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, sin…
Fast Optimistic Gradient Descent Ascent (OGDA) method in continuous and discrete time
Radu Ioan Bot, Ernö Robert Csetnek, Dang-Khoa Nguyen
In the framework of real Hilbert spaces we study continuous in time dynamics as well as numerical algorithms for the problem of approaching the set of zeros of a single-valued mono…
Fast Augmented Lagrangian Method in the convex regime with convergence guarantees for the iterates
Radu Ioan Bot, Ernö Robert Csetnek, Dang-Khoa Nguyen
This work aims to minimize a continuously differentiable convex function with Lipschitz continuous gradient under linear equality constraints. The proposed inertial algorithm resul…
Improved convergence rates and trajectory convergence for primal-dual dynamical systems with vanishing damping
Radu Ioan Bot, Dang-Khoa Nguyen
In this work, we approach the minimization of a continuously differentiable convex function under linear equality constraints by a second-order dynamical system with asymptotically…
A proximal minimization algorithm for structured nonconvex and nonsmooth problems
Radu Ioan Bot, Ernö Robert Csetnek, Dang-Khoa Nguyen
We propose a proximal algorithm for minimizing objective functions consisting of three summands: the composition of a nonsmooth function with a linear operator, another nonsmooth f…
The proximal alternating direction method of multipliers in the nonconvex setting: convergence analysis and rates
Radu Ioan Bot, Dang-Khoa Nguyen
We propose two numerical algorithms in the fully nonconvex setting for the minimization of the sum of a smooth function and the composition of a nonsmooth function with a linear op…