numerical algorithm – Optimization Online

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

Fast Moreau Envelope Computation I: Numerical Algorithms

Published: 2005/10/05, Updated: 2007/01/08

Yves Lucet

Convex Optimization, Nonsmooth Optimization, Problem Solving Environments conjugate, discrete legendre transform, envelope of functions, legendre-fenchel transform, linear-time worst-case complexity, moreau-yosida approximate, numerical algorithm

The present article summarizes the state of the art algorithms to compute the discrete Moreau envelope, and presents a new linear-time algorithm, named NEP for NonExpansive Proximal mapping. Numerical comparisons between the NEP and two existing algorithms: The Linear-time Legendre Transform (LLT) and the Parabolic Envelope (PE) algorithms are performed. Worst-case time complexity, convergence results, … Read more

NLPQLP: A New Fortran Implementation of a Sequential Quadratic Programming Algorithm

Published: 2002/01/10

Klaus Schittkowski

Constrained Nonlinear Optimization, Optimization Software Benchmark, Parallel Algorithms distributed computing, fortran code, line-search, nonlinear programming, numerical algorithm, performance evaluation, sequential quadratic programming

The Fortran subroutine NLPQLP solves smooth nonlinear programming problems and is an extension of the code NLPQL. The new version is specifically tuned to run under distributed systems. A new input parameter l is introduced for the number of parallel machines, that is the number of function calls to be executed simultaneously. In case of … Read more