zbMATH — the first resource for mathematics

A truncated Newton method with non-monotone line search for unconstrained optimization. (English) Zbl 0632.90059
An unconstrained minimization algorithm is defined, in which a non- monotone line search technique is employed in association with a truncated Newton algorithm. Numerical results obtained for a set of standard test problems are reported which indicate that the proposed algorithm is highly effective in the solution of ill-conditioned as well as of large dimensional problems.
Reviewer: L.Grippo

90C30 Nonlinear programming
49M15 Newton-type methods
65K05 Numerical mathematical programming methods
49M37 Numerical methods based on nonlinear programming
Full Text: DOI
[1] Moré, J. J., andSorensen, D. C.,Newton’s Method, Studies in Numerical Analysis, Edited by G. H. Golub, Mathematical Association of America, Washington, DC, 1984.
[2] Dembo, R. S., andSteihaug, T.,Truncated-Newton Algorithms for Large-Scale Unconstrained Optimization, Mathematical Programming, Vol. 26, pp. 190-212, 1983. · Zbl 0523.90078
[3] Gill, P. E., andMurray, W.,Newton-Type Methods for Unconstrained and Linearly Constrained Optimization, Mathematical Programming, Vol. 7, pp. 311-350, 1974. · Zbl 0297.90082
[4] Wolfe, M. A.,Numerical Methods for Unconstrained Optimization, Van Nostrand-Reinhold, New York, New York, 1978. · Zbl 0379.65033
[5] Fletcher, R.,Practical Methods of Optimization, Vol. 1, John Wiley, New York, New York, 1980. · Zbl 0439.93001
[6] Bulteau, J. P., andVial, J. P.,A Restricted Trust Region Algorithm for Unconstrained Optimization, Journal of Optimization Theory and Applications, Vol. 47, pp. 413-435, 1985. · Zbl 0556.90075
[7] Dennis, J. E., andSchnabel, R. B.,Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1983. · Zbl 0579.65058
[8] Shultz, G. A., Schnabel, R. B., andByrd, R. H.,A Family of Trust-Region-Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties, SIAM Journal on Numerical Analysis, Vol. 22, pp. 47-67, 1985. · Zbl 0574.65061
[9] Steihaug, T.,The Conjugate Gradient Method and Trust Regions in Large Scale Optimization, SIAM Journal on Numerical Analysis, Vol. 20, pp. 626-637, 1983. · Zbl 0518.65042
[10] Hestenes, M. R.,Conjugate Direction Methods in Optimization, Springer-Verlag, New York, New York, 1980. · Zbl 0439.49001
[11] Chamberlain, R. M., Powell, M. J. D., Lemarechal, C., andPedersen, H. C.,The Watchdog Technique for Forcing Convergence in Algorithms for Constrained Optimization, Mathematical Programming Study, Vol. 16, pp. 1-17, 1982. · Zbl 0477.90072
[12] Grippo, L., Lampariello, F., andLucidi, S.,A Nonmonotone Line Search Technique for Newton’s Method, SIAM Journal on Numerical Analysis, Vol. 23, pp. 707-716, 1986. · Zbl 0616.65067
[13] Armijo, L.,Minimization of Functions Having Lipschitz-Continuous First Partial Derivatives, Pacific Journal of Mathematics, Vol. 16, pp. 1-3, 1966. · Zbl 0202.46105
[14] Dembo, R. S., Eisenstat, S. C., andSteihaug, T.,Inexact Newton Methods, SIAM Journal on Numerical Analysis, Vol. 19, pp. 400-408, 1982. · Zbl 0478.65030
[15] Garg, N. K., andTapia, N. K.,QDN: A Variable Storage Algorithm for Unconstrained Optimization, Department of Mathematical Sciences, Rice University, Technical Report, 1977.
[16] Dixon, L. C. W., andPrice, R. C.,Numerical Experience with the Truncated Newton Method, Numerical Optimization Centre, Hatfield Polytechnic, Technical Report No. 169, 1986.
[17] Miele, A., andCantrell, J. W.,Study on a Memory Gradient Method for the Minimization of Functions, Journal of Optimization Theory and Applications, Vol. 3, pp. 459-470, 1969. · Zbl 0165.22702
[18] Moré, J. J., Garbow, B. S., andHillstrom, K. E.,Testing Unconstrained Optimization Software, ACM Transactions on Mathematical Software, Vol. 7, pp. 17-41, 1981. · Zbl 0454.65049
[19] Leon, A.,A Comparison Among Eight Known Optimizing Procedures, Recent Advances in Optimization Techniques, Edited by A. Lavi and T. Vogl, John Wiley, New York, New York, 1966.
[20] McCormick, G. P.,Nonlinear Programming, John Wiley and Sons, New York, New York, 1983.
[21] Luenberger, D. G.,Linear and Nonlinear Programming, Addison-Wesley, Reading, Massachusetts, 1984. · Zbl 0571.90051
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.