带扰动项的梯度法与混合投影法的收敛性分析

刘茜;李梅霞;王长钰;

数学学报 ›› 2009 ›› Issue (02) : 155-164.

中国科学院数学与系统科学研究院期刊网
数学学报 ›› 2009 ›› Issue (02) : 155-164. DOI: 10.12386/A2009sxxb0042
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带扰动项的梯度法与混合投影法的收敛性分析

    刘茜;李梅霞;王长钰;
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Convergence Analysis of Perturbed Gradient Methods and Hybrid Projection Methods

    Qian LIU Department of Mathematics,Shandong Normal University,Ji'nan 250014,P.R.China Mei Xia LI Department of Mathematics,Weifang College,Weifang 261041,P.R.China Chang Yu WANG Institute of Operations Research,Qufu Normal University,Qufu 273165,P.R.China
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摘要

对无约束最优化问题提出了带扰动项的梯度法与混合投影法.我们在很一般的条件下,证明了由算法产生的迭代点列{x_k}满足:要么f(x_k)→-∞,要么f(x_k)收敛于有限值且▽f(x_k)→0.当f(x)是伪凸函数时,由带扰动项的混合投影算法产生的迭代点列{x_k}将收敛于问题的一个最优解以及其他一些精细的收敛性质.

Abstract

For unconstrained optimization problem,we present perturbed gradient methods and hybrid projection methods.Under general conditions,we show that either f(x_k)→-∞or f(x_k) converges to a finite value and▽f(x_k)→0.If f(·) is quasi-convex,the perturbed projection methods force the sequence of iterates to a solution of the problem and some extended convergence results can be obtained.

关键词

梯度方法 / 扰动项 / 混合投影方法 / 收敛性

Key words

convergence / hybrid projection method / gradient method / perturbation

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刘茜;李梅霞;王长钰;. 带扰动项的梯度法与混合投影法的收敛性分析. 数学学报, 2009(02): 155-164 https://doi.org/10.12386/A2009sxxb0042
Qian LIU Department of Mathematics,Shandong Normal University,Ji'nan 250014,P.R.China Mei Xia LI Department of Mathematics,Weifang College,Weifang 261041,P.R.China Chang Yu WANG Institute of Operations Research,Qufu Normal University,Qufu 273165,P.R.China. Convergence Analysis of Perturbed Gradient Methods and Hybrid Projection Methods. Acta Mathematica Sinica, Chinese Series, 2009(02): 155-164 https://doi.org/10.12386/A2009sxxb0042

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