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.
Similar content being viewed by others
References
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
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
Burke J.V. and Han S.P. (1989). A robust SQP method. Math. Program. 43: 277–303
Du D.Z., Pardalos P.M. and Wu W.L. (2001). Mathematical Theory of Optimization. Kluwer Academic Publishers, Boston
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
Fletcher R. and Leyffer S. (2002). Nonlinear programming without a penalty function. Math. Program. 91: 239–269
Fletcher R., Leyffer S. and Toint P.L. (2002). On the global convergence of a filter-SQP algorithm. SIAM J. Optim. 13: 44–59
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
Han S.P. (1976). Superlinearly convergence variable metric algorithm for general nonlinear programming problems. Math. Program. 11: 263–282
Nie P.Y. and Ma C.F. (2006). A trust region filter mehtod for general nonlinear programming. Appl. Math. Comput. 172: 1000–1017
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
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)
Zhang J.L. and Zhang X.S. (2001). A modified SQP method with nonmonotone linesearch technique. J. Global Optim. 21: 201–218
Zhou G.L. (1997). A modified SQP method and its global convergence. J. Global Optim. 11: 193–205
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
Zhu Z.B. (2005). A globally and superlinearly convergent feasible QP-free method for nonlinear programming. Appl. Math. Comput. 168: 519–539
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Su, K. A globally and superlinearly convergent modified SQP-filter method. J Glob Optim 41, 203–217 (2008). https://doi.org/10.1007/s10898-007-9219-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-007-9219-0