Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems  

作　　者：You Zhao Xing He Mingliang Zhou Tingwen Huang 

机构地区：[1]Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing,College of Electronic and Information Engineering,Southwest University,Chongqing 400715,China [2]School of Computer Science,Chongqing University,Chongqing 400044,China [3]Department of Mathematics,Texas A&M University at Qatar,Doha 23874,Qatar [4]IEEE

出　　处：《IEEE/CAA Journal of Automatica Sinica》2024年第6期1485-1498,共14页自动化学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(62176218,62176027);the Fundamental Research Funds for the Central Universities(XDJK2020TY003);the Funds for Chongqing Talent Plan(cstc2024ycjh-bgzxm0082)。

摘　　要：The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.

关 键 词：Accelerated projection neurodynamic approach lin-ear and set constraints projection operators smooth and nonsmooth convex optimization time scaling. 

分 类 号：O224[理学—运筹学与控制论]