×

zbMATH — the first resource for mathematics

An adaptive truncation criterion, for linesearch-based truncated Newton methods in large scale nonconvex optimization. (English) Zbl 07064413
Summary: Starting from the paper by the third author and A. Sofer [ibid. 9, No. 4, 219–221 (1990; Zbl 0706.90073)], we propose a heuristic adaptive truncation criterion for the inner iterations within linesearch-based truncated Newton methods. Our aim is to possibly avoid “over-solving” of the Newton equation, based on a comparison between the predicted reduction of the objective function and the actual reduction obtained. A numerical experience on unconstrained optimization problems highlights a satisfactory effectiveness and robustness of the adaptive criterion proposed, when a residual-based truncation criterion is selected.

MSC:
90 Operations research, mathematical programming
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Caliciotti, A.; Fasano, G.; Nash, S.; Roma, M., Data and performance profiles applying an adaptive truncation criterion, within linesearch-based truncated Newton methods, in large scale nonconvex optimization, Data Brief, (2017), (in press)
[2] Conn, A. R.; Gould, N. I.M.; Toint, P. L., LANCELOT: A Fortran Package for Large-Scale Nonlinear Optimization (Release A), (1992), Springer Verlag Heidelberg, Berlin · Zbl 0761.90087
[3] A.R. Conn, N.I.M. Gould, P.L. Toint, Trust-region methods, MPS-SIAM Series on Optimization, Philadelphia, PA, 2000. · Zbl 0958.65071
[4] Dembo, R.; Eisenstat, S.; Steihaug, T., Inexact Newton methods, SIAM J. Numer. Anal., 19, 400-408, (1982) · Zbl 0478.65030
[5] Dembo, R.; Steihaug, T., Truncated-Newton algorithms for large-scale unconstrained optimization, Math. Program., 26, 190-212, (1983) · Zbl 0523.90078
[6] Eisenstat, S.; Walker, H., Globally convergent inexact Newton methods, SIAM J. Optim., 4, 393-422, (1994) · Zbl 0814.65049
[7] Eisenstat, S.; Walker, H., Choosing the forcing term in an inexact Newton method, SIAM J. Sci. Stat. Comput., 17, 16-32, (1996) · Zbl 0845.65021
[8] Fasano, G.; Roma, M., Iterative computation of negative curvature directions in large scale optimization, Comput. Optim. Appl., 38, 81-104, (2007) · Zbl 1171.90549
[9] Fasano, G.; Roma, M., Preconditioning newton—krylov methods in nonconvex large scale optimization, Comput. Optim. Appl., 56, 253-290, (2013) · Zbl 1314.90063
[10] Fasano, G.; Roma, M., A novel class of approximate inverse preconditioners for large scale positive definite linear systems in optimization, Comput. Optim. Appl., 65, 399-429, (2016) · Zbl 1369.90166
[11] Gould, N. I.M.; Orban, D.; Toint, P. L., cutest: A constrained and unconstrained testing environment with safe threads, Comput. Optim. Appl., 60, 545-557, (2015) · Zbl 1325.90004
[12] Izmailov, A. F.; Solodov, A. I.M., A truncated SQP method based on inexact interior-point solutions of subproblems, SIAM J. Optim., 20, 5, 2584-2613, (2010) · Zbl 1211.90233
[13] Lin, C.-J.; Moré, J., Newton’s method for large bound-constrained optimization problems, SIAM J. Optim., 9, 1100-1127, (1999) · Zbl 0957.65064
[14] Morales, J.; Nocedal, J., Automatic preconditioning by limited memory quasi-Newton updating, SIAM J. Optim., 10, 1079-1096, (2000) · Zbl 1020.65019
[15] J. Moré, S. Wright, Optimization Software Guide, SIAM - Frontiers in Applied Mathematics, Philadelphia, 1993.
[16] Nash, S., Truncated-Newton methods for large-scale function minimization, (Rauch, H., Applications of Nonlinear Programming To Optimization and Control, (1984), Pergamon Press Oxford), 91-100
[17] Nash, S., A survey of truncated-Newton methods, J. Comput. Appl. Math., 124, 45-59, (2000) · Zbl 0969.65054
[18] Nash, S.; Nocedal, J., A numerical study of the limited memory BFGS method and the truncated-Newton method for large scale optimization, SIAM J. Optim., 1, 358-372, (1991) · Zbl 0756.65091
[19] Nash, S.; Sofer, A., Assessing a search direction within a truncated-Newton method, Oper. Res. Lett., 9, 219-221, (1990) · Zbl 0706.90073
[20] Nash, S.; Sofer, A., A general-purpose parallel algorithm for unconstrained optimization, SIAM J. Optim., 1, 530-547, (1991) · Zbl 0754.90054
[21] Nocedal, J., Large scale unconstrained optimization, (Watson, A.; Duff, I., The State of the Art in Numerical Analysis, (1997), Oxford University Press Oxford), 311-338 · Zbl 0881.65055
[22] Schlick, T.; Fogelson, A., TNPACK - A truncated Newton package for large-scale problems: I. algorithm and usage, ACM Trans. Math. Software, 18, 46-70, (1992) · Zbl 0892.65030
[23] Schlick, T.; Fogelson, A., TNPACK - A truncated Newton package for large-scale problems: II. implementation examples, ACM Trans. Math. Software, 18, 71-111, (1992) · Zbl 0892.65031
[24] Xie, D.; Schlick, T., Efficient implementation of the truncated-Newton algorithm for large-scale chemistry applications, SIAM J. Optim., 10, 132-154, (1999) · Zbl 0956.65049
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.