• 论文 • 上一篇    下一篇

求解非线性互补问题的一类光滑Broyden-like方法

范斌1, 马昌凤1, 谢亚君2   

  1. 1. 福建师范大学数学与计算机科学学院, 福州 350007;
    2. 福建江夏学院信息系, 福州 350108
  • 收稿日期:2012-09-06 出版日期:2013-05-15 发布日期:2013-05-13
  • 通讯作者: 马昌凤
  • 基金资助:

    国家自然科学基金(11071041, 11201074)项目; 福建省自然科学基金(2013J01003)项目.

范斌, 马昌凤, 谢亚君. 求解非线性互补问题的一类光滑Broyden-like方法[J]. 计算数学, 2013, 35(2): 181-194.

Fan Bin, Ma Changfeng, Xie Yajun. A NONMONOTONE BROYDEN-LIKE METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS[J]. Mathematica Numerica Sinica, 2013, 35(2): 181-194.

A NONMONOTONE BROYDEN-LIKE METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS

Fan Bin1, Ma Changfeng1, Xie Yajun2   

  1. 1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China;
    2. Department of Information, Fujian jiangxia University, Fuzhou 350108, China)
  • Received:2012-09-06 Online:2013-05-15 Published:2013-05-13
非线性互补问题可以等价地转换为光滑方程组来求解. 基于一种新的非单调线搜索准则, 提出了求解非线性互补问题等价光滑方程组的一类新的非单调光滑 Broyden-like 算法.在适当的假设条件下, 证明了该算法的全局收敛性与局部超线性收敛性. 数值实验表明所提出的算法是有效的.
The nonlinear complementarity problems can reformulated as a smoothing system of equations. By using a new nonmonotone line search, a new nonmonotone smoothing Broydenlike algorithm is presented for solving nonlinear complementarity problems. The global and local superlinear convergence of the proposed algorithm are proved under suitable conditions. Some numerical examples are given to illustrate the performance and efficiency of the presented algorithm.

MR(2010)主题分类: 

()
[1] Harker P T, Pang J S. Finite-Dimensional Vriational Inequality and Nonlinear ComplementarityProblem: A Survey of Theory, Algorithms and Applications[J]. Math. Program, 1900, 48: 339-357.

[2] Feiring B R. A quadratic programming view of the linear complementary problem[J]. AppliedMathematics Letters, 1990, 3(3): 35-37.

[3] Fukushima M. Merit Functions for Variationial Inequality and Complementarity Problems[J].Nonlinear Optimization and Applicationis, Plenum Press, 1996, 155-170.

[4] Ferris M C, Pang J S. Engineering and Economic Applications of Complementarity Problems[J].SIAM Review, 1997, 39: 669-713.

[5] 韩继业, 修乃华, 戚厚铎. 非线性互补理论与算法[M]. 上海: 上海科学技术出版社, 2006.

[6] Li D H, Yamashita N, Fukushima M. Nonsmooth equation based BFGS method for solving KKTsystems in mathematical programming[J]. J Optim Theory Appl. 2001, 109(1): 123-167.

[7] Li D H, Fukushima M. A derivative-free line search and global convergence of Broyden-like methodfor nonlinear equations[J]. Optim Meth Software, 2000, 13(3): 181-201.

[8] Ma C, Chen L, Wang D. A globally and superlinearly convergent smoothing Broyden-like methodfor solving nonlinear complementarity problem[J]. Appl Math Comp., 2008, 198: 592-604.

[9] Ma C, Chen X, Tang J. On convergence of a smoothing Broyden-like method for P0-NCP[J].Nonlinear Anal: Real World Appl, 2008, 9: 899-911.

[10] Chen B, Ma C. A new smoothing Broyden-like method for solving nonlinear complementarityproblem with a P0-function[J]. Journal of Global Optimization, 2011, 51: 473-495.

[11] Chen B, Harker P T. A non-interior-point continuation method for linear complementarity problems[J]. SIAM J Matrix Anal Appl, 1993, 14: 1168-1190.

[12] Sun D. A regularization Newton method for solving nonlinear complementarity problems[J]. AppliedMathematics and Optimization, 1999, 40: 315-339.

[13] Kanzow C. Global convergence properties of some iterative methods for linear complementarityproblems[J]. SIAM J Optim, 1996, 6: 326-341.

[14] Pang J S, Qi L. Nonsmooth equations: Motivation and algorithms[J]. SIAM J Optim, 1993, 3:443-465.

[15] Pieraccini S, Gasparo M G, Pasquali A. Global Newton-type methods and semismooth reformulationsfor NCP[J]. Applied Numerical Mathematics, 2003, 44: 367-384.

[16] Dirkse S, Ferris M. MCPLIB: a collection of nonlinear mixed complementarity problems[J]. OptimMethods Softw, 1995, 5: 319-45.

[17] Ruggiero M A G, Martnez J M, Santos S A. Solving nonsmooth equations by means of quasi-Newton methods with globalization[J]. in: Recent Advances in Nonsmooth Optimization, WorldScientific, Singapore, 1995, 121-140.

[18] Spedicato E, Huang Z. Numerical experience with Newton-like methods for nonlinear algebraicsystems[J], Computing, 1997, 58: 69-89.
[1] 尹江华, 简金宝, 江羡珍. 凸约束非光滑方程组一个新的谱梯度投影算法[J]. 计算数学, 2020, 42(4): 457-471.
[2] 张纯, 贾泽慧, 蔡邢菊. 广义鞍点问题的改进的类SOR算法[J]. 计算数学, 2020, 42(1): 39-50.
[3] 闫熙, 马昌凤. 求解矩阵方程AXB+CXD=F参数迭代法的最优参数分析[J]. 计算数学, 2019, 41(1): 37-51.
[4] 李郴良, 田兆鹤, 胡小媚. 一类弱非线性互补问题的广义模系矩阵多分裂多参数加速松弛迭代方法[J]. 计算数学, 2019, 41(1): 91-103.
[5] 王福胜, 张瑞. 不等式约束极大极小问题的一个新型模松弛强次可行SQCQP算法[J]. 计算数学, 2018, 40(1): 49-62.
[6] 刘金魁. 解凸约束非线性单调方程组的无导数谱PRP投影算法[J]. 计算数学, 2016, 38(2): 113-124.
[7] 刘亚君, 刘新为. 无约束最优化的信赖域BB法[J]. 计算数学, 2016, 38(1): 96-112.
[8] 简金宝, 尹江华, 江羡珍. 一个充分下降的有效共轭梯度法[J]. 计算数学, 2015, 37(4): 415-424.
[9] 袁敏, 万中. 求解非线性P0互补问题的非单调磨光算法[J]. 计算数学, 2014, 36(1): 35-50.
[10] 简金宝, 唐菲, 黎健玲, 唐春明. 无约束极大极小问题的广义梯度投影算法[J]. 计算数学, 2013, 35(4): 385-392.
[11] 黄娜, 马昌凤, 谢亚君. 求解非对称代数Riccati 方程几个新的预估-校正法[J]. 计算数学, 2013, 35(4): 401-418.
[12] 毕亚倩, 刘新为. 求解界约束优化的一种新的非单调谱投影梯度法[J]. 计算数学, 2013, 35(4): 419-430.
[13] 刘金魁. 两种有效的非线性共轭梯度算法[J]. 计算数学, 2013, 35(3): 286-296.
[14] 孙清滢, 段立宁, 陈颖梅, 王宣战, 宫恩龙, 徐胜来. 基于修正拟牛顿方程的两阶段步长非单调稀疏对角变尺度梯度投影算法[J]. 计算数学, 2013, 35(2): 113-124.
[15] 简金宝, 马鹏飞, 徐庆娟. 不等式约束优化一个基于滤子思想的广义梯度投影算法[J]. 计算数学, 2013, 35(2): 205-214.
阅读次数
全文


摘要