非线性不等式系统带折线步的信赖域方法及其收敛性

何郁波; 林晓艳

doi:10.3879/j.issn.1000-0887.2013.11.011

非线性不等式系统带折线步的信赖域方法及其收敛性

doi: 10.3879/j.issn.1000-0887.2013.11.011

怀化学院数学与应用数学系, 湖南怀化 418008

基金项目: 湖南省教育厅资助重点项目(08A503);湖南省普通高校青年骨干教师培养基金资助项目(湘教通\[2012\]510号)

详细信息

作者简介:
何郁波,男,讲师,硕士(通讯作者. E-mail: heyinprc@yahoo.com.cn);林晓艳,女,教授,博士(E-mail: xiaoyanlin98@hotmail.com).

中图分类号: O178.2
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出版历程
- 收稿日期: 2013-04-09
- 修回日期: 2013-06-19
- 刊出日期: 2013-11-15

On the Convergence of Trust Region Method With Dogleg Step for Nonlinear Inequalities Systems

Department of Mathematics, Huaihua University, Huaihua, Hunan 418008, P.R.China

摘要

摘要: 针对一类非线性不等式系统求解的问题，利用一系列目标函数二次可微的带参数优化问题来逐次逼近非线性不等式系统的解，从而提出了针对参数最优化问题带折线步的信赖域算法．在较弱的条件下，算法的全局收敛性得到了保证．数值试验显示算法有效．
- 非线性不等式系统 /
- 信赖域算法 /
- Cauchy点 /
- 折线步 /
- 全局收敛
Abstract: The solutions of a class of nonlinear inequalities were studied.The nonlinear inequalities were approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions, then a smoothing trust region method with dogleg steps was applied to solve the parameterized optimization problems.The global convergence of the proposed method was established under some weak conditions. Numerical results show that the method performs well.
- nonlinear inequalities /
- trust region method /
- Cauchy point /
- dogleg step /
- global convergence

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参考文献(9)

[1]	Fukushima M. A finitely convergent algorithm for convex inequalities[J]. IEEE Trans Autom Contr,1982, 27(5): 1126-1127.
[2]	Jian J B, Liang Y M. Finitely convergent algorithm of generalized gradient projection for systems of nonlinear inequalities[J].Neural Parallel and Scientific Computing,2004, 12(2): 207-218.
[3]	JIAN Jinbao, CHENG Weixin, KE Xiaoyan. Finitely convergent ε-generalized projection algorithm for nonlinear systems[J]. J Math Anal Appl,2007, 332(2): 1446-1459.
[4]	何郁波, 马昌凤. 非线性不等式组的信赖域算法[J]. 工程数学学报, 2008, 25(2): 224230.(HE Yubo, MA Changfeng. Trust region method for nonlinear inequalities[J]. Journal of Engineering Mathematics,2008, 25(2): 224-230.(in Chinese))
[5]	何郁波, 林晓艳, 董晓亮. 非线性不等式组的光滑近似方法及其收敛性[J]. 应用数学学报, 2011, 34(4): 723-733.(HE Yu-bo, LIN Xiao-yan, DONG Xiao-liang. On the convergence of smoothing approximate method for nonlinear inequalities[J]. Acta Mathematicae Applicatae Sinica,2011, 34(4): 723733.(in Chinese))
[6]	Ma C F. A globally convergent LevenbergMarquardt method for the least l2-norm solution of nonlinear inequalities[J]. Applied Mathematics and Computation,2008, 206(1): 133-140.
[7]	程维新, 陈永强. 求解非线性不等式组的有限步终止算法[J]. 河南师范大学学报(自然科学版), 2010, 38(2): 25-27.(CHENG Wei-xin, CHEN Yong-qiang. A finitely terminating algorithm for systems of nonlinear inequalities[J]. Journal of Henan Normal University(Natural Science),2010, 38(2): 25-27.(in Chinese))
[8]	Powell M J D. Convergence properties of a class of minimization algorithms[C]//Mangasarian O L, Meyer P R, Robinson S M, Nonlinear Programming ed.2. New York: Academic Press, 1975.
[9]	Hock W, Schittkowski K. Test Examples for Nonlinear Programming Codes[M]. Berlin: SpringerVerlag Press, 1981.

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非线性不等式系统带折线步的信赖域方法及其收敛性

doi: 10.3879/j.issn.1000-0887.2013.11.011

作者简介:
何郁波,男,讲师,硕士(通讯作者. E-mail: heyinprc@yahoo.com.cn);林晓艳,女,教授,博士(E-mail: xiaoyanlin98@hotmail.com).

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On the Convergence of Trust Region Method With Dogleg Step for Nonlinear Inequalities Systems

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非线性不等式系统带折线步的信赖域方法及其收敛性

doi: 10.3879/j.issn.1000-0887.2013.11.011

作者简介: 何郁波,男,讲师,硕士(通讯作者. E-mail: heyinprc@yahoo.com.cn);林晓艳,女,教授,博士(E-mail: xiaoyanlin98@hotmail.com).

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出版历程

On the Convergence of Trust Region Method With Dogleg Step for Nonlinear Inequalities Systems

计量

出版历程

目录

作者简介:
何郁波,男,讲师,硕士(通讯作者. E-mail: heyinprc@yahoo.com.cn);林晓艳,女,教授,博士(E-mail: xiaoyanlin98@hotmail.com).