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非线性互补约束均衡问题的改进SQP算法

An improved SQP algorithm for mathematical programs with nonlinear complementarity constraints
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摘要 为了对可行序列二次规划算法进行研究与创新,利用逐步逼近思想,对互补约束条件光滑化,将均衡问题等价转化为一个光滑的标准非线性规划问题,进而利用序列二次规划算法思想求解。给出了SQP算法中辅助方向的存在性分析和具体求解方法,使算法更加合理可行。 In this thesis,we make an investigation on feasible sequential quadratic programming algorithm.At first,complementary constraints are smoothed with the idea of successive approximation,and the mathematical programming with equilibrium constraints is changed equivalently a standard smooth nonlinear programming.Then,the smooth nonlinear programming is solved by the idea of above-mentioned sequential quadratic programming algorithms.The existence and detailed solution procedure of the auxiliary direction for the SQP method is presented,which makes the existing algorithm more reasonable and feasible.
作者 耿振杰 朱志斌 黄青群
机构地区 桂林电子科技大学数学与计算科学学院 河池学院数学系
出处 《桂林电子科技大学学报》 2011年第6期494-497,共4页 Journal of Guilin University of Electronic Technology
基金 国家自然科学基金(11061011) 广西高校优秀人才资助计划项目([2009]156)
关键词 非线性互补约束均衡问题 SQP算法 MFCQ条件 Schur-补 MPEC SQP algorithm MFCQ condition Schur complement
分类号 O221.2 [理学—运筹学与控制论]
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参考文献10

  • 1朱志斌,简金宝,张聪.非线性互补约束均衡问题的一个SQP算法[J].应用数学和力学,2009,30(5):613-622. 被引量：9
  • 2JIANG H, RALPH D. Smooth SQP method for mathematical programs with nonlinear complementarity constraints [J]. SIAM J Optimization, 2000,10 (3) : 779-808.
  • 3FUKUSHIMA M, LUO Z Q, PANG J S. A globally convergent sequential quadratic programming algorithmfor mathematical programs with linear complementarity constraints v. Comp Opti Appl,1998, 10(1) :5-34.
  • 4MAC F, LIANG G P. A new successive approximation damped Newton method for nonlinear complementarity problems [J]. Journal of Mathematical Research a nd Exposition, 2003, 23 (1):1-6.
  • 5GAO Z Y, HE G P, WU F. Sequential Systems of Linear Equa- tions Algorithm for Nonlinear Optimization Problems with Gen- eral Constraints. Journal of Optimization Theory and Applications, 1997, 95(2) :371-397.
  • 6JIANG H Y, RALPH D. Extension of Quasi-newton Methodsto Mathematical Programs with Complementarity Constraints [J]. Computational Optimizationand Applications, 2003,25 : 123-150.
  • 7ZHU Z B, ZHANG K C. A superlinearly convergent SQP algo- rithm for mathematical programs with linear complementarity constraints [J]. Applied Mathematics and Computation, 2006, 172(1) : 222-244.
  • 8FACCHINEI F, LUCIDI S. Quadraticly and superlinearly con- vergent for the solution of inequality constrained optimization problem[J]. J Optim Theory Appl, 1995,85 (2) : 265-289.
  • 9PANIER 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.
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二级参考文献10

  • 1Outrate J V, Kocvare M, Zowe J. Nonsmooth Approach to Optimization Problems With Equilibrium Consrtaints[ M]. The Netherlands: Kluwer Academic Publishem, 1998.
  • 2Jiang H, Ralph D. Smooth SQP method for mathematical programs with nonlinear complementarity constraints[ J ]. SIAM J Optimization, 2000,10(3) : 779-808.
  • 3Fukushima 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.
  • 4Fukushima M, Pang J S. Some feasibility issues in mathematical programs with equilibrium constraints[J]. SIAMJ Optimization, 1998,8(3) : 673-581.
  • 5Panier E R, Tits A L. On combining feasibility, descent and superlinear convergence in inequality constrained optimization[ J]. Mathematical Programming, 1993,59(1) : 261-276.
  • 6Zhu Z B, Zhang K C. A superlineariy convergent SQP algorithm for mathematical programs with linear complementarity constraints[ J]. Applied Mathematics and Computation ,2005,172(1) : 222-244.
  • 7Panier E R, Tits A L. A stoerlinearly convergent feasible method for the solution of inequality constrained optimization problems[J]. SIAM J Control Optim, 1987,25(3) : 934-950.
  • 8Facchinei F, Dacidi S. Quadraticly and superlinearly convergent for the solution of inequality constrained op optimization problem[ J]. J Optim Theory Appl, 1995,85(2 ): 265-289.
  • 9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. 被引量：4
  • 10马昌凤,梁国平.求解非线性互补问题的逐次逼近阻尼牛顿法(英文)[J].Journal of Mathematical Research and Exposition,2003,23(1):1-6. 被引量：1

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桂林电子科技大学学报
2011年 第6期

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