Composite-step like filter methods for equality constraint problems

Journal of Computational Mathematics

Volumn 21, Issue 5, 2003, Pages 613-624

  Nie, Pu Yan ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

Composite step like approaches; Convergence; Equality constraints; Filter methods; Normal component; Sequential quadratic programming(SQP) algorithms; Tangential component

Indexed keywords

CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS;

COMPOSITE STEP LIKE APPROACHES; EQUALITY CONSTRAINTS; FILTER METHODS; NORMAL COMPONENT; SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHMS; TANGENTIAL COMPONENT;

ALGORITHMS;

EID: 0742266954     PISSN: 02549409     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. C. Audet and J.E. Dennis J., Combining pattern search and filter algorithms for derivative free optimization, TROO-9 Department of Computational and Applied Mathematics, Rice University, Houston, TX, 2000.
2. M.S. Bazara and C.M. Shetty, Nonlinear Programming theory and algorithms, John Wiley and Sons (1979).
3. R.H. Byrd, J.Ch. Gilbert and J. Nocedal, A trust region method based on interior point techniques for nonlinear programming, Math. Prog., 89 (2000), 149-185.
4. R.H. Byrd, M.E. Hribar and J. Nocedal, An interior point algorithm for large scale nonlinear programming, SIAM J. Optimization, 9 (1998), 877-900.
5. R.H. Byrd, R.B. Schnabel and G.A. Schultz, A trust region algorithm for nonlinearly constrained optimization, SIAM Journal on Numerical Analysis, 24 (1987), 1152-1170.
6. J.E. Dennis Jr, M. El-Alem, M.C. Maciel, A global convergence theory for general trust region based algorithms for equality constrained optimization, SIAM J. Opt., 7 (1997), 177-207.
7. J.E. Dennis Jr, R.B. Schnable, Numerical methods for unconstrained optimization and nonlinear equations, Prentice-Hall, Englewood Cliffs, NJ.
8. R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function, Math. Prog., 91:2 (2002), 239-269.
9. R. Fletcher, S. Leyffer and P.L. Toint, On the global convergence of an SLP-filter algorithm. Tech. Report. NA/183, Department of Mathematics, University of Dundee, 1998.
10. R. Fletcher and S. Leyffer, User manual for filter SQP. Tech. Report, NA/181, Department of Mathematics, University of Dundee, 1998.
11. R. Fletcher, S. Leyffer and Ph.L. Toint, On the global convergence of a SQP-filter algorithm, SIAM J. Optimization, 13 (2003), 44-59.
12. R. Fletcher and S. Leyffer, A bundle filter method for nonsmooth nonlinear optimization, Tech. Report, NA/195, Department of Mathematics, University of Dundee, 1999.
13. M. Lalee, J. Nocedal and T.D. Plantenga, On the implementation of an algorithm for large-scale equality constrained optimization, SIAM Journal on Optimization, 8:3 (1998), 682-706.
14. E.O. Omojokun, Trust region algorithm for optimization with nonlinear equality and inequality constraints, PhD thesis, University of Colorado, Boulder, Colorado, USA, 1989.
15. T.D. Plantenga, A trust-region method for nonlinear programming based on primal interior point techniques, SIAM journal on Scientific Computing, 20:1, 285-305.
16. M.J.D. Powell and Y. Yuan, A recursive quadratic programming algorithm for equality constrained optimization, Math. Prog., 35 (1986), 265-278.
17. V. Torczon, On the convergence of pattern search algorithms, SIAM. J. Optim., 7 (1997), 1-25.
18. M. Ulbrich, S. Ulbrich and L.N. Vicente, A globally convergent primal-dual interior-point filter method for nonconvex nonlinear programming, TROO-12 Department of Computational and Applied Mathematics, Rice University, Houston, TX, 2000.
19. A. Vardi, A trust region algorithm for equality constrained minimization: convergence and implementation, SIAM Journal on Numerical Analysis, 22:3 (1985), 575-591.
20. Y. Yuan, A null space algorithm for constrained optimization, Report, In Z.C. Shi et. al eds. Advance in Scientific Computing (Science Press, Beijing, 2001), 210-218.