Global convergence on an active set SQP for inequality constrained optimization

Journal of Computational and Applied Mathematics

Volumn 180, Issue 1, 2005, Pages 201-211

  Liu, Xin Wei ^a,b  

^a HEBEI UNIVERSITY OF TECHNOLOGY   (China)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Active set; Nonlinearly constrained optimization; Sequential quadratic programming

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; OPTIMIZATION; SET THEORY;

ACTIVE SET; NONLINEARLY CONSTRAINED OPTIMIZATION; SEQUENTIAL QUADRATIC PROGRAMMING;

QUADRATIC PROGRAMMING;

EID: 17644411998     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.10.012     Document Type: Article

References (24)

1. D.P. Bertsekas Constrained Optimization and Lagrange Multipliers 1982 Academic Press New York
2. M.C. Biggs Constrained minimization using recursive equality quadratic programming, in: F.A. Lootsma (Eds.) Numerical Methods for Nonlinear Optimization 1972 Academic Press New York 411-428
3. J.V. Burke S.P. Han A robust sequential quadratic programming method Math. Programming 43 1989 277-303
4. R. Fletcher Practical Methods of Optimization Second ed. 1987 Wiley Chichester
5. R. Fletcher, S. Leyffer, D. Ralph, S. Scholtes, Local convergence of SQP methods for mathematical programs with equilibrium constraints, Numerical Analysis Report NA/209, Department of Mathematics, University of Dundee, 2002.
6. Ph.E. Gill W. Murray M.H. Wright Practical Optimization 1981 Academic Press New York
7. S.P. Han A globally convergent method for nonlinear programming J. Optim. Theory. Appl. 22 1977 297-309
8. S.P. Han J.S. Pang N. Rangaraj Globally convergent Newton methods for nonsmooth equations Math. Oper. Res. 17 1992 586-607
9. C. Kanzow, An active set-type Newton method for constrained nonlinear systems, Complementarity: Applications, Algorithms and Extensions (Madison, WI, 1999), Applications in Optimizations, vol. 50, Kluwer Academic Publishers, Dordrecht, 2001, pp. 179-200.
10. K. Kunisch A. Rösch Primal-dual active set strategy for a general class of constrained optimal control problems SIAM J. Optim. 13 2002 321-334
11. X.-W. Liu, Y. Yuan, Global convergence of an active set SQP algorithm, Research Report ICM-97-82, ICMSEC.
12. X.-W. Liu Y.-X. Yuan A robust algorithm for optimization with general equality and inequality constraints SIAM J. Sci. Comput. 22 2000 517-534
13. X.-W. Liu G. Zhao A decomposition method based on SQP for a class of multistage stochastic programs SIAM J. Optim. 14 2003 200-222
14. W. Murray F.J. Prieto A sequential quadratic programming algorithm using an incomplete solution of the subproblem SIAM J. Optim. 5 1995 590-640
15. J.S. Pang Serial and parallel computation of Karush-Kuhn-Tucker points via nonsmooth equations SIAM J. Optim. 4 1994 872-893
16. M.J.D. Powell A fast algorithm for nonlinearly constrained optimization calculations, in: G.A. Watson (Eds.) Proceedings of the 1977 Dundee Biennial Conference on Numerical Analysis 1978 Springer Berlin 144-157
17. M.J.D. Powell The convergence of variable metric methods for nonlinear constrained optimization calculations, in: O.L. Mangasarian R.R. Meyer S.M. Robinson (Eds.) Nonlinear Programming 3 1978 Academic Press New York 27-63
18. M.J.D. Powell Y. Yuan A recursive quadratic programming algorithm that using differentiable exact penalty function Math. Programming 35 1986 265-278
19. B.N. Pshenichny Danilin Numerical Methods in Extremal Problems 1978 Mir Publishers Moscow
20. K. Schittkowski NLPQL: A FORTRAN subroutine solving constrained nonlinear programming problems Ann. Oper. Res. 5 1986 485-500
21. J. Stoer, Principles of sequential quadratic programming methods for solving nonlinear programs, in: K. Schittkowski (Ed.), NATO ASI Series, vol. F15, Computational Mathematical Programming, Springer, Berlin.
22. K. Taji M. Fukushima A new merit function and a successive quadratic programming algorithm for variational inequality problems SIAM J. Optim. 6 1996 704-713
23. Y. Yuan, Numerical Methods for Nonlinear Programming, Modern Mathematics Series, Shanghai Scientific & Technical Publishers, 1993.
24. J.L. Zhang X.S. Zhang A robust SQP method for optimization with inequality constraints J. Comput. Math. 21 2003 247-256