Asymptotic for a second-order evolution equation with convex potential and vanishing damping term

被引：59

作者：

May, Ramzi ^{[1
]}

机构：

[1] King Faisal Univ, Coll Sci, Dept Math & Stat, Al Ahsaa, Saudi Arabia

来源：

TURKISH JOURNAL OF MATHEMATICS | 2017年 / 41卷 / 03期

关键词：

Dynamical systems; asymptotically small dissipation; asymptotic behavior; energy function; convex function; convex optimization;

D O I：

10.3906/mat-1512-28

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this short note, we recover by a different method the new result due to Attouch, Chbani, Peyrouqet, and Redont concerning the weak convergence as t -> +infinity of solutions x(t) to the second-order differential equation x" (t) + k/t x' (t) + del Phi(x(t)) = 0, where K > 3 and Phi is a smooth convex function defined on a Hilbert space H. Moreover, we improve their result on the rate of convergence of Phi(x(t)) min Phi.

引用

页码：681 / 685

页数：5

共 5 条

[1] Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity [J].