[en] In classical trust-region optimization algorithms, the radius of the trust region is reduced, kept constant, or enlarged after, respectively, unsuccessful, successful, and very successful iterations. We propose here to re. ne the empirical rules used for this update by the definition of a new set of iterations that we call "too successful iterations." At such iterations, a large reduction of the objective function is obtained despite a crude local approximation of the objective function; the trust region is thus kept nearly constant instead of being enlarged. The new update rules preserve the strong convergence property of traditional trust-region methods. They can also be generalized to define a self-adaptive trust-region algorithm along the lines introduced by Hei [J. Comput. Math., 21 (2003), pp. 229-236]. Numerical experiments carried out on 70 unconstrained problems from the CUTEr collection demonstrate the positive impact of the modified update strategy on the efficiency and robustness of quasi-Newton variants of a trust-region solver, when BFGS or SR1 updates of the approximation of the Hessian matrix are carried at all iterations.
Disciplines :
Mathematics
Author, co-author :
Walmag, J. M. B.
Delhez, Eric ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Mathématiques générales
Language :
English
Title :
A note on trust-region radius update
Publication date :
2005
Journal title :
SIAM Journal on Optimization
ISSN :
1052-6234
eISSN :
1095-7189
Publisher :
Society for Industrial & Applied Mathematics, Philadelphia, United States - Pennsylvania
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Bibliography
I. BONGARTZ, A. R. CONN, N. GOULD, AND P. L. TOINT, Constrained and unconstrained testing environment. ACM Trans. Math. Software, 21 (1995), pp. 123-160.
R. H. BYRD, H. F. KHALFAN, AND R. B. SCHNABEL, Analysis of a symmetric rank-one trust region method, SIAM J. Optim., 6 (1996), pp. 1025-1039.
A. R. CONN, N. I. M. GOULD, AND P. L. TOINT, Trust Region Methods, MPS/SIAM Ser. Optim. 1, SIAM, Philadelphia, 2000.
J. E. DENNIS AND H. H. W. MEI, Two new unconstrained optimization algorithms which use function and gradient values, J. Optim. Theory Appl., 28 (1979), pp. 453-482.
E. D. DOLAN AND J. J. MORÉ, Benchmarking optimization software with performance profiles, Math. Program., Series A, 91 (2002), pp. 201-213.
R. FLETOHER, Practical Methods of Optimization, 2nd ed., John Wiley & Sons, New York, 1987.
N. I. M. GOULD, S. LUCIDI, M. ROMA, AND P. L. TOINT, Solving the trust-region subproblem using the Lanczos method, SIAM J. Optim., 9 (1999), pp. 504-525.
N. I. M. GOULD. D. ORBAN, A. SARTENAER. AND P. L. TOINT, Sensitivity of trust-region algorithms to their parameters, 4OR, 3 (2005), pp. 227-241.
N. I. M. GOULD. D. ORBAN. AND P. L. TOINT, CUTEr (and SifDec), A constrained and unconstrained testing environment, revisited, Trans. Amer. Math. Soc. Math. Softw., 29 (2003), pp. 373-394.
L. HEI, A self-adaptive trust region algorithm, J. Comput. Math., 21 (2003), pp. 229-236.
J. M. MORÉ AND D. C. SORENSEN, Computing a trust region step, SIAM J. Sci. Statist. Comput., 4 (1983), pp. 553-572.
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