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Combining trust region and linesearch algorithm for equality constrained optimization

  • Zhensheng Yu
  • Changyu Wang
  • Jiguo Yu
Article

Abstract

In this paper, a combining trust region and line search algorithm for equality constrained optimization is proposed. At each iteration, we only need to solve the trust region subproblem once, when the trust region trial step can not be accepted, we switch to line search to obtain the next iteration. Hence, the difficulty of repeated solving trust region subproblem in an iterate is avoided. In order to allow the direction of negative curvature, we add second correction step in trust region step and employ nommonotone technique in line search. The global convergence and local superlinearly rate are established under certain assumptions. Some numerical examples are given to illustrate the efficiency of the proposed algorithm.

AMS Mathematics Subject Classification

90C30 65K05 

Keywords and phrases

Trust region line search global convergence local superlinearly rate 

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References

  1. 1.
    R.H. Byrd, R.B. Schnabel, G.A. Schultz,A trust region algorithm for nonlinearly constrained optimization, SIAM J. Numerical Analysis, 24 (1987), No. 6, 1152–1169.MATHCrossRefGoogle Scholar
  2. 2.
    J.E. Dennis, L.N. Vicente,On the convergence theory of trust-region-based algorithms for equality constrained optimization, SIAM J. Optim., 7 (1997), No. 4, 927–950.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    M.J.D. Powell and Y. Yuan,A trust region algorithm for equality constrained optimization, Mathematical Programming, 49 (1991), No. 2, 189–211.MathSciNetGoogle Scholar
  4. 4.
    A. Vardi,A trust region algorithm for equality constrained minimization convergence properties and implemention, SIAM J. Numerical Analysis. 22 (1985), No. 3, 575–591.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    A.R. Conn, N.I.M. Gould and P.L. Toint,Trust region methods, MPS/SIAM Series on Optimization, Society for Industrial and Applied Mathematics(SIAM), Philadelphia, PA. 2000.MATHGoogle Scholar
  6. 6.
    M. Fukushima,A successive quadratic programming algorithm with global and superlinear convergence properties, Mathematical Programming, 35 (1986), No. 3, 253–264.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    E.O. Omojokun,Trust region algorithm for optimization with equalities and inequalities constraints, Ph.D. Thesis, University of Cororado at Boulder, 1989.Google Scholar
  8. 8.
    Y.L. Lai, Z.Y. Gao, G.P. He,A generalized gradient projection algorithm of optimization with nonlinear constraints, Science in China(Series A), 36 (1993), No. 2, 170–180.MATHMathSciNetGoogle Scholar
  9. 9.
    J. Nocedal, Y. Yuan,Combining trust region and line search techniques, in Yuan Y. ed., Advance in nonlinear programming, 1998, 153–176.Google Scholar
  10. 10.
    J.Z. Zhang and D.T. Zhu,A trust region dogleg method for nonlinear optimization, Optimization 21 (1990), 543–557.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    J. Nocedal and M.L. Overton,Projection Hessian updating method for nonlinear constrained optimization, SIAM J. Numer. Anal, 22 (1985), No. 5, 821–850.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    L. Gripp, F. Lampariello, S. Lucidi,A nonmonotone line search technique for Newton's methods, SIAM J. Numer. Anal., 23 (1986), No. 4, 707–716.CrossRefMathSciNetGoogle Scholar
  13. 13.
    T.F. Coleman A.R. Conn,Nonlinear programming via an exact penalty function: asymptotic analysis, Mathematical programming, 24 (1982), No. 2, 123–136.MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    E.R. Panier and A.L. tits,Avoiding Maratos effect by means of nonmonotone line search constrained problems, SIAM J. Numer. Anal., 28 (1991), No. 4, 1183–1190.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 2004

Authors and Affiliations

  1. 1.Department of Apllied MathematicsDalian University of TechnologyDalianP. R. China
  2. 2.Institute of Operations Research of Qufu Normal UniversityQufuP. R. China
  3. 3.Department of Computer of Qufu Normal UniversityQufuP. R. China

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