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改进的无约束优化问题的过滤算法

A Improved Filter Method For Unconstrained Optimization
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摘要 信赖域算法加入过滤技术可以加大试验点xk+被接受的几率.文章去除了信赖域子问题凸性的判断,同时对于信赖域半径采用自适应的选取办法,使信赖域半径与gk和Bk密切相关,以求对于信赖域算法的改进. Trust-region methods join filter technology can increase the possibility of trial point x＋k accepted.We leave out the judgement of the convexity of the trust-region subproblem,meanwhile use adaptive selection method,and make trust region radius closely related with gk and Bk in order to improve the traditional trust region algorithm.
作者 段凤奇 王川龙
机构地区 太原理工大学数学系
出处 《太原师范学院学报（自然科学版）》 2011年第1期28-31,共4页 Journal of Taiyuan Normal University:Natural Science Edition
基金 山西省自然科学基金资助(20051009)
关键词 无约束 滤子 信赖域 自适应 unconstrained optimization filter trust-region methods self-adapting
分类号 O221.2 [理学—运筹学与控制论]
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参考文献5

  • 1Powell M J D.On the global convergen of trust region algorithms for unconstrained optimization[J].Mathematical programming,1984,29(3):297-303.
  • 2Fletcher R,Leyffer S.Nonlinear programming without a penalty function[J].Mathematics programming,1997,91(2):239-270.
  • 3NIM Gould,Sainvitu C,Toint Ph L.A filter-trust-region method for unconstrained optimization[J].SIAM Journal on Optimization,2006,16(2):341-357.
  • 4缪卫华,孙文瑜.一个解无约束优化问题的过滤信赖域方法[J].高等学校计算数学学报,2007,29(1):88-96. 被引量：22
  • 5Deng N Y,Xiao Y,Zhu D.A nonmonotone trust region algorithm[J].Optimiz Theory Appi,1993,76:259-285.

二级参考文献17

  • 1Conn A R, Gould N I M, Toint Ph L. Trust region methods. SIAM, Philadelphia, USA, 2000
  • 2Deng N Y, Xiao Y, Zhu D. A nonmonotone trust region algorithm. J. Optimiz. Theory Appl., 1993, 76:259-285
  • 3Fletcher R, Gould N I M, Toint Ph L. Global convergence of trust-region SQP filter algorithm for general nonlinear programming. Technical Report RAL-TR-1999-041, Computational Sicence and Engineering Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, England, UK, 1999
  • 4Fletcher R, Leyffer S. Nonlinear programming without a penalty function. Technical Report NA/171, Department of Mathematics, University of Dundee, Dundee, Scotland, 1997
  • 5Fletcher R, Leyffer S, Toint Ph L. On the global convergence of a filter-SQP algorithm. Technical Report NA/197, Department of Mathematics, University of Dundee, Dundee, Scotland, 2000
  • 6Gould N I M, Leyffer S, Toiut Ph L. A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares. Technical Report RAL-TR-2003-004, Computational Sicence and Engineering Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, England, UK, 2003
  • 7Gould N I M, Lucidi S, Roma M, Toint Ph L. Solving the trust-region subproblem using the Lanczos method. SIAM J. Optimiz., 1999, 9(2): 504-525
  • 8Gould N I M, Sainvitu C, Toint Ph L. A filter-trust-region method for unconstrained optimization. Technical Report RAL-TR-2004-009, Computational Sicence and Engineering Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, England, UK, 2004
  • 9More J J, Sorensen D C. Computing a trust-region step. SIAM J. Sci. Statist. Comput., 1983, 4:553-572
  • 10Nocedal J, Wright S J. Numerical optimization. Springer, New York, 1999

共引文献21

太原师范学院学报（自然科学版）
2011年 第1期

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