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整体收敛的非线性等式约束优化问题的不精确修正正割方法
  • ISSN号：1000-5137
  • 期刊名称：《上海师范大学学报：自然科学版》
  • 时间：0
  • 分类：O224[理学—运筹学与控制论;理学—数学]
  • 作者机构：[1]上海师范大学数理学院,上海200234, [2]上海师范大学商学院,上海200234
  • 相关基金：The authors gratefully acknowledge the partial supports of the National Science Foundation Grant （ 10871130） and the Ph. D. Foundation Grant （20093127110005 ） of Chinese Education Ministry.
作者： 蔡力[1], 朱德通[2]
关键词： Fletcher罚函数, 约束优化, 正割算法, 不精确方法, 收敛性, Fletcher＇s penalty function , constrained optimization , secant method , inexact method , convergence
中文摘要：

通过使用线搜索技术，提出了一类具有整体收敛性的不精确修正正割算法解非线性约束优化问题．引入Fletcher罚函数作为价值函数克服了产生Maratos效应．在合理条件下证明了该类算法具有二步q阶超线性收敛速率．进而，对于约束进行很小的额外计算改进了此类算法，以使新算法具有一步q阶超线性收敛速率．数值实验的结果证明了该算法的有效性和可行性．

英文摘要：

We propose a class of modified global convergent inexact secant methods in association with line search technique for solving nonlinear constrained optimization problems. By introducing Fletcher＇s penalty function as a merit function, the Maratos effect can be avoided. The resulting algorithms possess global convergence while maintaining two - step q - superlinear local convergence rates under some reasonable conditions. Furthermore, with one extra evaluation of the constraints at each iteration, the improved algorithms have one - step q - superlinear local convergence rates. The results of numerical experiments indicate that the proposed algorithms are efficient for the given test problems.

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期刊信息
  • 《上海师范大学学报：自然科学版》
  • 中国科技核心期刊
  • 主管单位:上海市教育委员会
  • 主办单位:上海师范大学
  • 主编：丛玉豪
  • 地址：上海市桂林路100号
  • 邮编：200234
  • 邮箱：xuebao@shnu.edu.cn
  • 电话：021-64322304
  • 国际标准刊号：ISSN：1000-5137
  • 国内统一刊号：ISSN：31-1416/C
  • 邮发代号:4-655
  • 获奖情况:
  • 2010年获教育部“中国科技论文在线优秀期刊”二等奖,2011年获中国高校科技期刊研究会第二届全国高师学...,2013年获中国高校科技期刊研究会高师学报系统的“...
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  • 德国数学文摘,中国中国科技核心期刊
  • 被引量:3487