Abstract
In this paper, an unconstrained minimization algorithm is defined in which a nonmonotone 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 illconditioned as well as of large dimensional problems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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.
Dembo, R. S., andSteihaug, T.,Truncated-Newton Algorithms for Large-Scale Unconstrained Optimization, Mathematical Programming, Vol. 26, pp. 190–212, 1983.
Gill, P. E., andMurray, W.,Newton-Type Methods for Unconstrained and Linearly Constrained Optimization, Mathematical Programming, Vol. 7, pp. 311–350, 1974.
Wolfe, M. A.,Numerical Methods for Unconstrained Optimization, Van Nostrand-Reinhold, New York, New York, 1978.
Fletcher, R.,Practical Methods of Optimization, Vol. 1, John Wiley, New York, New York, 1980.
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.
Dennis, J. E., andSchnabel, R. B.,Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1983.
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.
Steihaug, T.,The Conjugate Gradient Method and Trust Regions in Large Scale Optimization, SIAM Journal on Numerical Analysis, Vol. 20, pp. 626–637, 1983.
Hestenes, M. R.,Conjugate Direction Methods in Optimization, Springer-Verlag, New York, New York, 1980.
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.
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.
Armijo, L.,Minimization of Functions Having Lipschitz-Continuous First Partial Derivatives, Pacific Journal of Mathematics, Vol. 16, pp. 1–3, 1966.
Dembo, R. S., Eisenstat, S. C., andSteihaug, T.,Inexact Newton Methods, SIAM Journal on Numerical Analysis, Vol. 19, pp. 400–408, 1982.
Garg, N. K., andTapia, N. K.,QDN: A Variable Storage Algorithm for Unconstrained Optimization, Department of Mathematical Sciences, Rice University, Technical Report, 1977.
Dixon, L. C. W., andPrice, R. C.,Numerical Experience with the Truncated Newton Method, Numerical Optimization Centre, Hatfield Polytechnic, Technical Report No. 169, 1986.
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.
Moré, J. J., Garbow, B. S., andHillstrom, K. E.,Testing Unconstrained Optimization Software, ACM Transactions on Mathematical Software, Vol. 7, pp. 17–41, 1981.
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.
McCormick, G. P.,Nonlinear Programming, John Wiley and Sons, New York, New York, 1983.
Luenberger, D. G.,Linear and Nonlinear Programming, Addison-Wesley, Reading, Massachusetts, 1984.
Author information
Authors and Affiliations
Additional information
Communicated by L. C. W. Dixon
Rights and permissions
About this article
Cite this article
Grippo, L., Lampariello, F. & Lucidi, S. A truncated Newton method with nonmonotone line search for unconstrained optimization. J Optim Theory Appl 60, 401–419 (1989). https://doi.org/10.1007/BF00940345
Issue Date:
DOI: https://doi.org/10.1007/BF00940345