nesterov’s accelerated gradient method

Fast convergence of the primal-dual dynamical system and algorithms for a nonsmooth bilinearly coupled saddle point problem

Published: 2024/03/23, Updated: 2024/03/25

Game Theory, Nonsmooth Optimization convergence rate, nesterov's accelerated gradient method, numerical algorithm, primal-dual dynamical system, saddle point problem

This paper is devoted to study the convergence rates of a second-order dynamical system and its corresponding discretizations associated with a nonsmooth bilinearly coupled convex-concave saddle point problem. We derive the convergence rate of the primal-dual gap for the second-order dynamical system with asymptotically vanishing damping term. Based on the implicit discretization, we propose a … Read more

Fast convergence of inertial primal-dual dynamics and algorithms for a bilinearly coupled saddle point problem

Published: 2023/09/19, Updated: 2024/03/25

Phan Vuong

Convex Optimization convergence rates, Damped inertial dynamics, Iterates convergence, nesterov's accelerated gradient method, numerical algorithm, saddle point problem

This paper is devoted to study the convergence rates of a second-order dynamical system and its corresponding discretization associated with a continuously differentiable bilinearly coupled convex-concave saddle point problem. First, we consider the second-order dynamical system with asymptotically vanishing damping term and show the existence and uniqueness of the trajectories as global twice continuously differentiable … Read more

An Accelerated Minimal Gradient Method with Momentum for Convex Quadratic Optimization

Published: 2021/05/05

Oscar S. Dalmau

Rafael Herrera

Harry Oviedo

Convex Optimization, Unconstrained Optimization conjugate-gradient methods, gradient methods, nesterov's accelerated gradient method

In this article we address the problem of minimizing a strictly convex quadratic function using a novel iterative method. The new algorithm is based on the well–known Nesterov’s accelerated gradient method. At each iteration of our scheme, the new point is computed by performing a line–search scheme using a search direction given by a linear … Read more

An optimal control theory for accelerated optimization

Published: 2019/02/24, Updated: 2019/05/19

Isaac Ross

Convex and Nonsmooth Optimization, Unconstrained Optimization accelerated newton's method, control lyapunov function, lie derivative, nesterov's accelerated gradient method, polyak's heavy ball method, riemannian metric, transversality mapping principle

Accelerated optimization algorithms can be generated using a double-integrator model for the search dynamics imbedded in an optimal control problem. CitationunpublishedArticleDownload View PDF

Nonsmooth Algorithms and Nesterov’s Smoothing Techniques for Generalized Fermat-Torricelli Problems

Published: 2013/07/22, Updated: 2014/05/07

Convex and Nonsmooth Optimization generalized fermat-torricelli problem, mm principle, nesterov's accelerated gradient method, subgradient-type algorithms

In this paper we present some algorithms for solving a number of new models of facility location involving sets which generalize the classical Fermat-Torricelli problem. Our approach uses subgradient-type algorithms to cope with nondierentiabilty of the distance functions therein. Another approach involves approximating nonsmooth optimization problems by smooth optimizations problems using Nesterov’s smoothing techniques. Convergence … Read more