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一个求解不可微凸优化的新算法

A New Algorithm for Nondifferentiable Convex Optimization
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摘要 该文结合文献[1]Chen和Fukushima的邻近点拟牛顿方法和过滤集技术,给出了一个求解不可微凸优化问题的新算法.与Chen和Fukushima的方法不同,新算法不用线搜索,而是用过滤集构造接受准则,并借助于过滤集技术,证明了算法的整体收敛性. A new algorithm for nondifferentiable convex optimization, combining the proximal quasi-Newton method with filter methods, is presented in this paper. The new algorithm uses the filter instead of using the line searching method to accept the trial step, so it is different from proximal quasi-Newton method. The global convergence of the new algorithm has been proved in this study.
作者 后六生
机构地区 南京晓庄学院数学与信息技术学院
出处 《南京晓庄学院学报》 2012年第6期8-12,共5页 Journal of Nanjing Xiaozhuang University
关键词 非光滑凸优化 邻近点方法 拟牛顿方法 过滤集 捆集 nondifferentiable convex optimization proximal point method quasi-Newton method filter bundle
分类号 O221.2 [理学—运筹学与控制论]
  • 相关文献

参考文献8

  • 1Chen Xiaojun, Fukushima M. Proximal quasi-Newton methods for nondifferentiable convex optimization [ J 1- Math. Program, 1999,85:313 - 334.
  • 2Hiriart-Urruty J. B. , Lemareehal C. Convex analysis and minimization algorithm[ M ]. Springer Verlag Heidelberg, 1993.
  • 3袁亚湘,孙文瑜.最优化理论和方法[M].北京:科学出版社,1997.
  • 4Fletcher R. , Leyffer S. Nonlinear programming without a penalty function[ J]. Math. Program, 2002, 91:239 -269.
  • 5Chen C. A new trust region based SLP filter algorithm which uses EQP active set strategy[ Z]. PhD Thesis, Mathematics Dept. , Univ. of Dundee. 2001.
  • 6Fletcher R. , Leyffer S. , Toint P.L.. On the global convergence of a fiher-SQP algorithm[J]. SIAM J. Optim. 2002, 13:44 59.
  • 7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
  • 8Fukushima M.. A descent algorithm for nonsmooth convex Optimization [ J ] Math. Program, 1984,30:63 - 175.

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30

南京晓庄学院学报
2012年 第6期

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