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带扰动项的FR共轭梯度法
  • 期刊名称：运筹学学报12：2（2008），1-16
  • 时间：0
  • 分类：O242.23[理学—计算数学;理学—数学] O175.27[理学—数学;理学—基础数学]
  • 作者机构：[1]潍坊学院数学系,山东潍坊261061, [2]山东师范大学数学系,山东济南250014, [3]曲阜师范大学运筹所,山东曲阜273165
  • 相关基金：This work is supported by National Natural Science Foundation under Grant No.10571106.
  • 相关项目：广义半无限规划的理论与算法研究
关键词： 运筹学, 无约束最优化, 共轭梯度法, 全局收敛性, 扰动, Operations research, unconstrained optimization, conjugate gradient method, global convergence, data perturbations
中文摘要：

本文提出了两种搜索方向带有扰动项的Fletcher—Reeves（abbr．FR）共轭梯度法．其迭代公式为xk＋1=xk＋αk（sk＋ωk），其中sk由共轭梯度迭代公式确定，ωk为扰动项，αk采用线搜索确定而不是必须趋于零．我们在很一般的假设条件下证明了两种算法的全局收敛性，而不需要目标函数有下界或水平集有界等有界性条件．

英文摘要：

In this paper, we propose two kinds of Fletcher-Reeves （abbr.FR） conjugate gradient methods with linesearch in the case that the search direction is perturbed slightly. Their iterate formula is xk＋1 = xk ＋ αk（sk ＋ ωk）, where the main direction sk is obtained by FR conjugate gradient method and ωk is perturbation term. The stepsize αk is determined by linesearch and needs not tend to zero. We prove that the two kinds of methods are globally convergent under mild conditions, and in doing so, we remove various boundedness conditions such as boundedness from blow of f, boundedness of level set, etc.

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