Related papers: Nesterov Acceleration for Equality-Constrained Con…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
In this paper we present a complete iteration complexity analysis of inexact first order Lagrangian and penalty methods for solving cone constrained convex problems that have or may not have optimal Lagrange multipliers that close the…
Nesterov's accelerated gradient (AG) is a popular technique to optimize objective functions comprising two components: a convex loss and a penalty function. While AG methods perform well for convex penalties, such as the LASSO, convergence…
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…
Convergence analysis of accelerated first-order methods for convex optimization problems are presented from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient flow, has…
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…
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…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
We introduce a generic scheme to solve nonconvex optimization problems using gradient-based algorithms originally designed for minimizing convex functions. Even though these methods may originally require convexity to operate, the proposed…
We present a totally asynchronous algorithm for convex optimization that is based on a novel generalization of Nesterov's accelerated gradient method. This algorithm is developed for fast convergence under "total asynchrony," i.e., allowing…
We develop two new proximal alternating penalty algorithms to solve a wide range class of constrained convex optimization problems. Our approach mainly relies on a novel combination of the classical quadratic penalty, alternating…
In this paper, we study a variant of the quadratic penalty method for linearly constrained convex problems, which has already been widely used but actually lacks theoretical justification. Namely, the penalty parameter steadily increases…
We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective…
Motivated by an inertial primal-dual dynamical system with vanishing damping, we propose a class of accelerated augmented Lagrangian methods with Nesterov extrapolation parameters for a linearly constrained convex optimization problem with…
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…
This paper addresses a distributed convex optimization problem with a class of coupled constraints, which arise in a multi-agent system composed of multiple communities modeled by cliques. First, we propose a fully distributed…
We derive an equivalent form of Halpern's fixed-point iteration scheme for solving a co-coercive equation (also called a root-finding problem), which can be viewed as a Nesterov's accelerated interpretation. We show that one method is…
We propose a new method for unconstrained optimization of a smooth and strongly convex function, which attains the optimal rate of convergence of Nesterov's accelerated gradient descent. The new algorithm has a simple geometric…
We propose an adaptive smoothing algorithm based on Nesterov's smoothing technique in \cite{Nesterov2005c} for solving "fully" nonsmooth composite convex optimization problems. Our method combines both Nesterov's accelerated proximal…
In convex optimization, continuous-time counterparts have been a fruitful tool for analyzing momentum algorithms. Fewer such examples are available when the function to minimize is non-convex. In several cases, discrepancies arise between…