互补约束均衡问题一个新的磨光技术

朱志斌; 罗志军; 曾吉文

互补约束均衡问题一个新的磨光技术

桂林电子科技大学计算科学与数学系,广西桂林 541004;2.厦门大学数学科学学院,福建厦门 361005

基金项目: 国家自然科学基金资助项目(10501009;60471039);广西自然科学基金资助项目(0728206);中国博士后基金资助项目(20070410227)

详细信息

作者简介:
朱志斌(1974- ),男,湖南双峰人,副教授,博士(联系人.+86-773-5608612;E-mail:zhuzb@guet.edu.cn).

中图分类号: O211
计量
- 文章访问数: 2457
- HTML全文浏览量: 69
- PDF下载量: 916
- 被引次数: 0
出版历程
- 收稿日期: 2006-07-05
- 修回日期: 2007-07-25
- 刊出日期: 2007-10-15

A New Smoothing Technique for Mathematical Programs With Equilibrium Constraints

Department of Computational Science and Mathematics, Guilin University of Electronic Technology, Guilin 541004, P. R. China;

摘要

摘要: 研究了一类带非线性互补约束的均衡问题．借助于逐步逼近思想,构造了一个在求解意义上与原问题等价的磨光非线性规划．从而保证一些经典的标准优化算法可以应用到该类优化问题上．最后提出了两个算法模型并分析了其全局收敛性．
- 均衡问题 /
- 非线性互补约束 /
- 原始-对偶稳定点 /
- 磨光方程组 /
- 全局收敛
Abstract: A kind of mathematical programs with equilibrium constraints(MPEC) is studied.By using the idea of successive approximation,a smoothing nonlinear programming,which is equivalent to the MPEC problem,was proposed.Thereby,it is ensured that some classical optimization methods can be applied for the MPEC problem.In the end,two algorithm models were proposed with the detailed analysis of the global convergence.
- mathematical program with equilibrium constraint /
- nonlinear complementarity constraint /
- primal-dual stationary point /
- smoothing system of equation /
- global convergence

HTML全文

参考文献(9)

[1]	Outrata J, Zowe J.A numerical approach to optimization problems with variational inequality constraints[J].Mathematical Programming,1995,68(1):105-130.
[2]	Luo Z Q,Pang J S,Ralph D,et al.Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints[J].Mathematical Programming,1996,75(1)：19-76.
[3]	Outrata J, Kocvare M,Zowe J.Nonsmooth Approach to Optimization Problems With Equilibrium Consraints[M].Netherlands: Kluwer Academic Publishers, 1998.
[4]	Facchinei F, Jiang H Y,Qi L.A smoothing method for mathematical programs with equilibjum constraints[J].Mathematical Programming,1999,85(1)：107-134. doi: 10.1007/s101070050048
[5]	李飞,徐成贤.求解带均衡约束数学规划问题的一个连续化方法[J].计算数学,2004,26(1)：3-12.
[6]	Fukushima M, Luo Z Q,Pang J S.A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints[J].Computational Optimization and Applications,1998,10(1)：5-34. doi: 10.1023/A:1018359900133
[7]	Qi L, Chen X J. A globally convergent successive approximation methods for non-smooth equation[J].SIAM Journal on Control and Optimization,1995,33(3)：402-418. doi: 10.1137/S036301299223619X
[8]	Ma C F,Liang G P.A new successive approximation damped Newton method for nonlinear complementarity problems[J].Journal of Mathematical Research and Exposition,2003,23(1)：1-6.
[9]	Luo Z Q, Pang J S, Ralph D.Mathematical Programs With Equilibrium Constraints[M].Cambridge：Cambridge University Press,1996.