Journal of Global Optimization

, Volume 41, Issue 2, pp 203–217

A globally and superlinearly convergent modified SQP-filter method

Article

Abstract

In this paper, we presented a modified SQP-filter method based on the modified quadratic subproblem proposed by Zhou (J. Global Optim. 11, 193–2005, 1997). In contrast with the SQP methods, each iteration this algorithm only needs to solve one quadratic programming subproblems and it is always feasible. Moreover, it has no demand on the initial point. With the filter technique, the algorithm shows good numerical results. Under some conditions, the globally and superlinearly convergent properties are given.

Keywords

Constrained optimization KKT point Sequential quadratic programming Global convergence Superlinear convergence 

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References

  1. 1.
    Boggs P.T., Tolle J.W. and Wang P. (1982). On the local convergence of quasi-newton methods for constrained optimization. SIAM J. Control Optim. 20: 161–171 CrossRefGoogle Scholar
  2. 2.
    Bonnons J.F., Painer E.R., Titts A.L. and Zhou J.L. (1992). Avoiding the Maratos effect by means of nonmontone linesearch, Inequality constrained problems-feasible iterates. SIAM J. Numer. Anal. 29: 1187–1202 CrossRefGoogle Scholar
  3. 3.
    Burke J.V. and Han S.P. (1989). A robust SQP method. Math. Program. 43: 277–303 CrossRefGoogle Scholar
  4. 4.
    Du D.Z., Pardalos P.M. and Wu W.L. (2001). Mathematical Theory of Optimization. Kluwer Academic Publishers, Boston Google Scholar
  5. 5.
    Facchinei F. and Lucidi S. (1995). Quadraticly and superlinearly convergent for the solution of inequality constrained optimization problem. J. Optim. Theory Appl. 85: 265–289 CrossRefGoogle Scholar
  6. 6.
    Fletcher R. and Leyffer S. (2002). Nonlinear programming without a penalty function. Math. Program. 91: 239–269 CrossRefGoogle Scholar
  7. 7.
    Fletcher R., Leyffer S. and Toint P.L. (2002). On the global convergence of a filter-SQP algorithm. SIAM J. Optim. 13: 44–59 CrossRefGoogle Scholar
  8. 8.
    Fletcher R., Gould N.I.M., Leyffer S., Toint P.L. and Wachter A. (2002). Global convergence of a trust region SQP-filter algorithm for general nonlinear programming. SIAM J. Optim. 13: 635–660 CrossRefGoogle Scholar
  9. 9.
    Han S.P. (1976). Superlinearly convergence variable metric algorithm for general nonlinear programming problems. Math. Program. 11: 263–282 CrossRefGoogle Scholar
  10. 10.
    Nie P.Y. and Ma C.F. (2006). A trust region filter mehtod for general nonlinear programming. Appl. Math. Comput. 172: 1000–1017 CrossRefGoogle Scholar
  11. 11.
    Powell M.J.D. (1978). A fast algorithm for nonlinear constrained optimization calculations. In: Waston, G.A. (eds) Numerical Analysis., pp 144–157. Springer-Verlag, Berlin CrossRefGoogle Scholar
  12. 12.
    Powell, M.J.D.: Variable metric methods for constrained optimization. In: Bachen, A., et al. (eds.) Mathematical Programming-The state of Art. Springer-Verlag, Berlin (1982)Google Scholar
  13. 13.
    Zhang J.L. and Zhang X.S. (2001). A modified SQP method with nonmonotone linesearch technique. J. Global Optim. 21: 201–218 CrossRefGoogle Scholar
  14. 14.
    Zhou G.L. (1997). A modified SQP method and its global convergence. J. Global Optim. 11: 193–205 CrossRefGoogle Scholar
  15. 15.
    Zhu Z.B., Zhang K.C. and Jian J.B. (2003). An improved SQP algorithm for inequality constrained optimization. Math. Methods Oper. Res. 58: 271–282 CrossRefGoogle Scholar
  16. 16.
    Zhu Z.B. (2005). A globally and superlinearly convergent feasible QP-free method for nonlinear programming. Appl. Math. Comput. 168: 519–539 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsTongji UniversityShangHaiP.R.China
  2. 2.College of Mathematics and ComputerHebei UniversityBaodingP.R.China

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