Related papers: From Halpern's Fixed-Point Iterations to Nesterov'…

We propose a framework to use Nesterov's accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously…

In this paper, we develop a new type of accelerated algorithms to solve some classes of maximally monotone equations as well as monotone inclusions. Instead of using Nesterov's accelerating approach, our methods rely on a so-called…

In this technical note, we are concerned with the problem of solving variational inequalities with improved convergence rates. Motivated by Nesterov's accelerated gradient method for convex optimization, we propose a Nesterov's accelerated…

We develop two "Nesterov's accelerated" variants of the well-known extragradient method to approximate a solution of a co-hypomonotone inclusion constituted by the sum of two operators, where one is Lipschitz continuous and the other is…

We analyze a modified version of Nesterov accelerated gradient algorithm, which applies to affine fixed point problems with non self-adjoint matrices, such as the ones appearing in the theory of Markov decision processes with discounted or…

Following the first part of our project, this paper comprehensively studies two types of extragradient-based methods: anchored extragradient and Nesterov's accelerated extragradient for solving [non]linear inclusions (and, in particular,…

Nesterov's well-known scheme for accelerating gradient descent in convex optimization problems is adapted to accelerating stationary iterative solvers for linear systems. Compared with classical Krylov subspace acceleration methods, the…

Alternating minimization (AM) procedures are practically efficient in many applications for solving convex and non-convex optimization problems. On the other hand, Nesterov's accelerated gradient is theoretically optimal first-order method…

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…

We consider unconstrained minimization of smooth convex functions. We propose a novel variational perspective using forced Euler-Lagrange equation that allows for studying high-resolution ODEs. Through this, we obtain a faster convergence…

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…

The Nesterov accelerated gradient method, introduced in 1983, has been a cornerstone of optimization theory and practice. Yet the question of its point convergence had remained open. In this work, we resolve this longstanding open problem…

We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov's accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov's scheme and thus can serve as a tool for analysis. We show…

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…

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…

We modify Nesterov's constant step gradient method for strongly convex functions with Lipschitz continuous gradient described in Nesterov's book. Nesterov shows that $f(x_k) - f^* \leq L \prod_{i=1}^k (1 - \alpha_k) \| x_0 - x^* \|_2^2$…

Despite their frequent slow convergence, proximal gradient schemes are widely used in large-scale optimization tasks due to their tremendous stability, scalability, and ease of computation. In this paper, we develop and investigate a…

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…

This work proposes an Accelerated Primal-Dual Fixed-Point (APDFP) method that employs Nesterov type acceleration to solve composite problems of the form min f(x) + g(Bx), where g is nonsmooth and B is a linear operator. The APDFP features…