非线性互补约束均衡问题的一个SQP算法

朱志斌; 简金宝; 张聪

doi:10.3879/j.issn.1000-0887.2009.05.012

非线性互补约束均衡问题的一个SQP算法

doi: 10.3879/j.issn.1000-0887.2009.05.012

桂林电子科技大学数学与计算科学学院,广西桂林 541004;2.广西大学数学与信息科学学院,南宁 530004

基金项目: 国家自然科学基金资助项目(10501009;10771040);广西壮族自治区自然科学基金资助项目(0728206;0640001);中国博士后基金资助项目(20070410228)

详细信息

作者简介:
朱志斌(1974- ),男,湖南双峰人,教授,博士(联系人.E-mail:zhuzbma@hotmail.com).

中图分类号: O221.2
计量
- 文章访问数: 1307
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- 被引次数: 0
出版历程
- 收稿日期: 2008-07-19
- 修回日期: 2009-02-27
- 刊出日期: 2009-05-15

An SQP Algorithm for Mathematical Programs With Nonlinear Complementarity Constraints

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

摘要

摘要: 提出了一个求解非线性互补约束均衡问题(MPCC)的逐步逼近光滑SQP算法．通过一系列光滑优化来逼近MPCC．引入l1精确罚函数,线搜索保证算法具有全局收敛性．进而,在严格互补及二阶充分条件下,算法是超线性收敛的．此外,当算法有限步终止,当前迭代点即为MPEC的一个精确稳定点．
- 均衡问题 /
- 序列二次规划算法 /
- 逐步逼近 /
- 全局收敛 /
- 超线性收敛速率
Abstract: A successive approximation and smooth SQP method for mathematical programs with nonlinear complementarity constraints (MPCC) is described. A class of smooth programs to approximate the MPCC was introduced. Using an l₁ penalty function, the line search assures the global convergence, while superlinear convergence rate is shown under strictly complementary conditions and the second order sufficient condition. Moreover, it was proved that the current iterated point is an exact stationary point of the MPEC when the algorithm terminates finitely.
- MPEC /
- SQP algorithm /
- successive approximation /
- global convergence /
- superlinear convergence rate

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参考文献(10)

[1]	Outrate J V, Kocvare M, Zowe J.Nonsmooth Approach to Optimization Problems With Equilibrium Consrtaints[M].The Netherlands: Kluwer Academic Publishers,1998.
[2]	Jiang H, Ralph D. Smooth SQP method for mathematical programs with nonlinear complementarity constraints[J].SIAM J Optimization,2000,10(3):779-808. doi: 10.1137/S1052623497332329
[3]	Fukushima M, Luo Z Q, Pang J S. A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints[J].Comp Opti Appl，1998,10(1):5-34. doi: 10.1023/A:1018359900133
[4]	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.
[5]	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[J].应用数学和力学,2007,28(10): 1253-1260.
[6]	Fukushima M, Pang J S. Some feasibility issues in mathematical programs with equilibrium constraints[J].SIAM J Optimization,1998,8(3): 673-681. doi: 10.1137/S105262349731577X
[7]	Panier E R, Tits A L. On combining feasibility, descent and superlinear convergence in inequality constrained optimization[J].Mathematical Programming,1993,59(1): 261-276. doi: 10.1007/BF01581247
[8]	Zhu Z B, Zhang K C. A superlinearly convergent SQP algorithm for mathematical programs with linear complementarity constraints[J].Applied Mathematics and Computation,2006,172(1): 222-244. doi: 10.1016/j.amc.2005.01.141
[9]	Panier E R, Tits A L. A superlinearly convergent feasible method for the solution of inequality constrained optimization problems[J].SIAM J Control Optim,1987,25(3): 934-950. doi: 10.1137/0325051
[10]	Facchinei F,Lucidi S. Quadraticly and superlinearly convergent for the solution of inequality constrained optimization problem[J].J Optim Theory Appl,1995,85(2): 265-289. doi: 10.1007/BF02192227