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A class of nonmonotone trust region algorithms for unconstrained optimization problems 被引量：2

A class of nonmonotone trust region algorithms for unconstrained optimization problems
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摘要 A class of nonmonotone trust region algorithms is presented for unconstrained optimizations. Under suitable conditions, the global and Q quadratic convergences of the algorithm are proved. Several rules of choosing trial steps and trust region radii are also discussed. A class of nonmonotone trust region algorithms is presented for unconstrained optimizations. Under suitable conditions, the global and Q quadratic convergences of the algorithm are proved. Several rules of choosing trial steps and trust region radii are also discussed.
作者 柯小伍 韩继业
出处 《Science China Mathematics》 SCIE 1998年第9期927-932,共6页 中国科学：数学（英文版）
基金 November 7 1997ProjectsupportedbytheNationalNaturalScienceFoundationofChina (GrantNo .19136 0 12 ) .
关键词 NONMONOTONE TRUST REGION algorithm global CONVERGENCE Q QUADRATIC CONVERGENCE UNCONSTRAINED optimization. nonmonotone, trust region algorithm, global convergence, Q quadratic convergence, unconstrained optimization.
分类号 O224 [理学—运筹学与控制论]
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参考文献11

  • 1Philippe L. Toint.Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints[J]. Mathematical Programming . 1997 (3)
  • 2L. Grippo,F. Lampariello,S. Lucidi.A truncated Newton method with nonmonotone line search for unconstrained optimization[J]. Journal of Optimization Theory and Applications . 1989 (3)
  • 3Richard H. Byrd,Robert B. Schnabel,Gerald A. Shultz.Approximate solution of the trust region problem by minimization over two-dimensional subspaces[J]. Mathematical Programming . 1988 (1-3)
  • 4Moré JJ,Bachem A,Grotschel M,Korte B.Recent developments in algorithms and software for trust region methods. Mathematical Programming: The State of the Art . 1983
  • 5R.H.Byrd,R.B.Schnabel,and CIA.Shultz.＂Approximate solutionof the trust region problem by minimization over two-dimensionalsubspaces＂. Mathematical Programming . 1988
  • 6Shultz G A,Schnabel R B,Byrd R H.A family of trust-region-based algorithms for unconstrained minimization with strong global convergence properties. SIAM Journal on Numerical Analysis . 1985
  • 7Grippo,L.,Lampariello,F.,Lucidi,S.A nonmonotone line search technique for Newton’s method. SIAM Journal on Numerical Analysis . 1986
  • 8Grippo,L.,Lampariello,F.,Lucidi,S.A truncated Newton method with nonmonotone line search for unconstrained optimization. Journal of Optimization Theory and Applications . 1989
  • 9Deng,N.Y.,Xiao,Y.,Zhou,F.J.A nonmonotonic trust region algorithm. Journal of Optimization . 1993
  • 10Toint,P. L.Nonmonotone trust-region algorithms for nonlinear optimization subject to convex constraints, Math. Prog . 1997

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Science China Mathematics
1998年 第9期

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