Nonmonotone curvilinear line search methods for unconstrained optimization

Computational Optimization and Applications

Volumn 6, Issue 2, 1996, Pages 117-136

  Ferris, M C ^a   Lucidi, S ^b   Roma, M ^b  

^a University of Wisconsin Madison   (United States)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; MATRIX ALGEBRA; OPTIMIZATION; PROBLEM SOLVING;

BUNCH-PARLETT DECOMPOSITION; CURVILINEAR LINESEARCH; HESSIAN MATRIX; NONMONOTONE STABILIZATION STRATEGY; UNCONSTRAINED MINIMIZATION PROBLEMS;

COMPUTATIONAL METHODS;

EID: 0030243966     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00249642     Document Type: Article

References (28)

1. M. Arioli, T.F. Chan, I.S. Duff, N.I.M. Gould, and J.K. Reid, "Computing a search direction for large-scale linearly-constrained nonlinear optimization calculations," Technical Report TR/PA/93/34, CERFACS, 1993.
2. I. Bongartz, A.R. Conn, N. Gould, and Ph.L. Toint, "CUTE: Constrained and unconstrained testing environment," Publications du Départment de Mathématique Report 93/10, Facultés Universitaires De Namur, 1993.
3. To appear in ACM Trans. Math. Soft.
4. J.R. Bunch and B.N. Parlett, "Direct methods for solving symmetric indefinite systems of linear equations," SIAM Journal on Numerical Analysis, vol. 8, pp. 639-655, 1971.
5. A.R. Conn, N.I.M. Gould, and Ph.L. Toint, "LANCELOT: A fortran package for large-scale nonlinear optimization (Release A)," Number 17 in Springer Series in Computational Mathematics, Springer Verlag, Heidelberg, Berlin, 1992.
6. R.S. Dembo and T. Steihaug, "Truncated Newton method algorithms for large-scale unconstrained optimization," Mathematical Programming, vol. 26, pp. 190-212, 1983.
7. N.Y. Deng, Y. Xiao, and F.J. Zhou, "Nonmonotonic trust region algorithm," Journal of Optimization Theory and Applications, vol. 76, pp. 259-285, 1993.
8. S.P. Dirkse and M.C. Ferris, "The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems," Optimization Methods & Software, vol. 5, pp. 123-156, 1995.
9. M.C. Ferris and S. Lucidi, "Nonmonotone stabilization methods for nonlinear equations," Journal of Optimization Theory and Applications, vol. 81, pp. 53-74, 1994.
10. A. Forsgren, P.E. Gill, and W. Murray, "A modified Newton method for unconstrained optimization," Technical Report SOL 89-12, Department of Operations Research, Stanford University: Stanford, California, 1989.
11. A. Forsgren, P.E. Gill, and W. Murray, "Computing modified Newton directions using a partial Cholesky factorization," Technical Report TRITA-MAT-1993-9, Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden, 1993.
12. P.E. Gill, W. Murray, D.B. Poncélon, and M.A. Saunders, "Preconditioners for indefinite systems arising in optimization," SIAM Journal on Matrix Analysis and Applications, vol. 13, pp. 292-311, 1992.
13. P.E. Gill and W. Murray, "Newton-type methods for unconstrained and linearly constrained optimization," Mathematical Programming, vol. 7, pp. 311-350, 1974.
14. L. Grippo, F. Lampariello, and S. Lucidi, "A nonmonotone line search technique for Newton's method," SIAM Journal on Numerical Analysis, vol. 23, pp. 707-716, 1986.
15. L. Grippo, F. Lampariello, and S. Lucidi, "A class of nonmonotone stabilization methods in unconstrained optimization," Numerische Mathematik, vol. 59, pp. 779-805, 1991.
16. G.P. McCormick, "A modification of Armijo's step-size rule for negative curvature," Mathematical Programming, vol. 13, pp. 111-115, 1977.
17. G.P. McCormick, Nonlinear Programming: Theory, Algorithms and Applications, John Wiley & Sons: New York, 1983.
18. J.J. Moré and D.C. Sorensen, "On the use of directions of negative curvature in a modified Newton method," Mathematical Programming, vol. 16, pp. 1-20, 1979.
19. S.G. Nash, "Newton-type minimization via Lanczos method," SIAM Journal on Numerical Analysis, vol. 21, pp. 770-788, 1984.
20. J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press: San Diego, California, 1970.
21. C.C. Paige and M.A. Saunders, "Solution of sparse indefinite systems of linear equations," SIAM Journal on Numerical Analysis, vol. 12, pp. 617-629, 1975.
22. T. Schlick, "Modified Cholesky factorization for sparse preconditioners," SIAM Journal on Scientific Computing, vol. 14, pp. 424-445, 1993.
23. R.B. Schnabel and E. Eskow, "A new modified Cholesky factorization," SIAM Journal on Scientific and Statistical Computing, vol. 11, pp. 1136-1158, 1990.
24. G.A. Shultz, R.B. Schnabel, and R.H. Byrd, "A family of trust-region-based algorithms for unconstrained minimization," SIAM Journal on Numerical Analysis, vol. 22, pp. 44-67, 1985.
25. Ph.L. Toint, "Towards an efficient sparsity exploiting Newton method for minimization," in I.S. Duff (Ed.), Sparse Matrices and Their Uses, Academic Press: London, pp. 57-88, 1981.
26. Ph.L. Toint, "An assesment of non-monotone linesearch techniques for unconstrained optimization," Technical Report 94/14, Department of Mathematics, FUNDP, Namur, Belgium, 1994.
27. Ph.L. Toint, "A non-monotone trust-region algorithm for nonlinear optimization subject to convex constraints," Technical Report 94/24, Department of Mathematics, FUNDP, Namur, Belgium, 1994.
28. Y. Xiao and F.J. Zhou, "Nonmonotone trust region methods with curvilinear path in unconstrained minimization," Computing, vol. 48, pp. 303-317, 1992.