FILTRANE, a Fortran 95 filter-trust-region package for solving nonlinear least-squares and nonlinear feasibility problems

ACM Transactions on Mathematical Software

Volumn 33, Issue 1, 2007, Pages

  Gould, Nicholas I M ^a,c   Toint, Philippe L ^b  

^a RUTHERFORD APPLETON LABORATORY   (United Kingdom)

^b UNIVERSITY OF NAMUR   (Belgium)

^c UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Filter methods; Nonlinear feasibility; Nonlinear least squares; Nonlinear systems

Indexed keywords

ALGORITHMS; LEAST SQUARES APPROXIMATIONS; NONLINEAR SYSTEMS; PARAMETER ESTIMATION; PROBLEM SOLVING;

FILTER METHODS; NONLINEAR FEASIBILITY; NONLINEAR LEAST-SQUARES;

FORTRAN (PROGRAMMING LANGUAGE);

EID: 33947710109     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/1206040.1206043     Document Type: Article

References (20)

1. CONN, A. R., GOULD, N. I. M., AND TOINT, PH. L. 2000. Trust-Region Methods. MPS-SIAM Series on Optimization, No. 01. SIAM, Philadelphia, USA.
2. DENNIS, J. E., GAY, D. M., AND WELSCH, R. E. 1981. An adaptive nonlinear least squares algorithm. ACM Trans. Math. Softw. 7, 3, 348-368.
3. DENNIS, J. E. AND SCHNABEL, R. B. 1983. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs, NJ.
4. Reprinted as Classics in Applied Mathematics 16, SIAM, Philadelphia, PA, 1996.
5. DOLAN, E. D. AND MORÉ, J. J. 2002. Benchmarking optimization software with performance profiles. Math. Programm. 91, 2, 201-213.
6. FLETCHER, R., GOULD, N. I. M., LEYFFER, S., TOINT, PH. L., AND WÄCHTER, A. 2002a. Global convergence of trust-region SQP-filter algorithms for nonlinear programming. SIAM J. Optimiz. 13, 3, 635-659.
7. FLETCHER, R. AND LEYFFER, S. 1998. User manual for filterSQP. Numerical analysis rep. NA/181. Department of Mathematics, University of Dundee, Dundee, Scotland.
8. FLETCHER, R. AND LEYFFER, S. 2002. Nonlinear programming without a penalty function. Math. Programm. 91, 2, 239-269.
9. FLETCHER, R., LEYFFER, S., AND TOINT, PH. L. 2002b. On the global convergence of a filter-SQP algorithm. SIAM J. Optimiz. 13, 1, 44-59.
10. GONZAGA, C. C., KARAS, E., AND VANTI, M. 2003. A globally convergent filter method for nonlinear programming. SIAM J. Optimiz. 14, 3, 646-669.
11. GOULD, N. I. M., LEYFFER, S., AND TOINT, PH. L. 2005. A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares. SIAM J. Optimiz. 15, 1, 17-38.
12. GOULD, N. I. M., LUCIDI, S., ROMA, M., AND TOINT, PH. L. 1999. Solving the trust-region subproblem using the Lanczos method. SIAM J. Optimiz. 9, 2, 504-525.
13. GOULD, N. I. M., ORBAN, D., AND TOINT, PH. L. 2003a. CUTEr, a constrained and unconstrained testing environment, revisited. ACM Trans. Math. Softw. 29, 4, 373-394.
14. GOULD, N. I. M., ORBAN, D., AND TOINT, PH. L. 2003b. GALAHAD - a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization. ACM Trans. Math. Softw. 29, 4, 353-372.
15. MORÉ, J. J. AND SORENSEN, D. C. 1983. Computing a trust region step. SIAM J. Sci. Statist. Comput. 4, 3, 553-572.
16. MORÉ, J. J. AND SORENSEN, D. C. 1984. Newton's method. In Studies in Numerical Analysis, G. H. Golub, Ed. MAA Studies in Mathematics, No. 24. American Mathematical Society, Providence, RI, 29-82.
17. NOCEDAL, J. 1984. Trust region algorithms for solving large systems of nonlinear equations. In Innovative Methods for Nonlinear Problems, W. Liu, T. Belytschko, and K. C. Park, Eds. Pineridge Press, Swansea, U. K. 93-102.
18. ORTEGA, J. M. AND RHEINBOLDT, W. C. 1970. Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, London, U. K.
19. TOINT, PH. L. 1986. Numerical solution of large sets of algebraic nonlinear equations. Math. Computat. 46, 173, 175-189.
20. TOINT, PH. L. 1987. On large scale nonlinear least squares calculations. SIAM J. Sci. Statist. Comput. 8, 3, 416-435.