求解无约束非线性规划问题的一个新的重开始共轭梯度算法的收敛性

数学季刊 ›› 2003, Vol. 18 ›› Issue (2): 154-162.

求解无约束非线性规划问题的一个新的重开始共轭梯度算法的收敛性

Department of Applied Mathematics,Dalian University of Technology,Dalian 116024,China;Depart- ment of Applied Mathematics,University of Petroleum,Dongying 257061,China

收稿日期:2001-10-30 出版日期:2003-06-30 发布日期:2024-04-16
作者简介:SUN Qing-ying(1966-),male,native of Qingzhou,Shandong,an associate professor of University of Petro- leum,M.S.D.,engages in nonlinear programming.

Global Convergence of a New Restarting Conjugate Gradient Method for Nonlinear Optimizations

Department of Applied Mathematics,Dalian University of Technology,Dalian 116024,China;Depart- ment of Applied Mathematics,University of Petroleum,Dongying 257061,China

Received:2001-10-30 Online:2003-06-30 Published:2024-04-16
About author:SUN Qing-ying(1966-),male,native of Qingzhou,Shandong,an associate professor of University of Petro- leum,M.S.D.,engages in nonlinear programming.

摘要/Abstract

摘要： Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions.In this note,by combining the nice numerical per- formance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991),a class of new restarting conjugate gradient methods is presented.Global convergences of the new method with two kinds of common line searches,are proved.Firstly,it is shown that,using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously differentiable function with Curry-Altman's step size rule and a bounded level set.Secondly,by using comparing technique, some general convergence propecties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method

关键词: nonlinear , programming;restarting , conjugate , gradient , method;forcing , function;reverse modulus of continuity function;convergence

Abstract: Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions.In this note,by combining the nice numerical per- formance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991),a class of new restarting conjugate gradient methods is presented.Global convergences of the new method with two kinds of common line searches,are proved.Firstly,it is shown that,using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously differentiable function with Curry-Altman's step size rule and a bounded level set.Secondly,by using comparing technique, some general convergence propecties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method

Key words: nonlinear , programming;restarting , conjugate , gradient , method;forcing , function;reverse modulus of continuity function;convergence

中图分类号:

O221.2

孙清滢. 求解无约束非线性规划问题的一个新的重开始共轭梯度算法的收敛性[J]. 数学季刊, 2003, 18(2): 154-162.

SUN Qing-ying. Global Convergence of a New Restarting Conjugate Gradient Method for Nonlinear Optimizations[J]. Chinese Quarterly Journal of Mathematics, 2003, 18(2): 154-162.