Reduced storage, Quasi-Newton trust region approaches to function optimization

SIAM Journal on Optimization

Volumn 10, Issue 1, 1999, Pages 56-69

  Kaufman, Linda ^a  

^a LUCENT TECHNOLOGIES   (United States)

Author keywords

Limited memory; Quasi Newton; Trust region

Indexed keywords

EID: 0033275992     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623496303779     Document Type: Article

References (17)

1. B. AVERICK, R. CARTER, AND J. MORÉ, The Minpack-2 Test Problem Collection, ANL-MCS-TM-150, Argonne National Laboratory, Argonne, IL, 1991.
2. A. BUCKLEY AND A. LENIR QN-like variable storage conjugate gradients. Math. Programming, 27 (1983), pp. 155-175.
3. J. BURKE AND A. WIEGMANN, Notes on limited memory BFGS updating in a trust-region framework, SIAM J. Optim., submitted.
4. R. BYRD, J. NOCEDAL, AND R. SCHNABEL, Representation of quasi-Newton matrices and their use in limited memory methods, Math. Programming, 63 (1994), pp. 129-156.
5. J. DANIEL, W. GRAGG, L. KAUFMAN, AND G.W. STEWART, Stable algorithms for updating the Gram-Schmidt QR factorization, Math. Comp., 30 (1976), pp. 772-795.
6. J. DENNIS, D. GAY, AND R. WELSCH, Algorithm 611 subroutines for unconstrained minimization using a model/trust-region approach, ACM Trans. Math. Software, 9 (1983), pp. 503-524.
7. J. DENNIS AND H. MEI, An unconstrained optimization algorithm which uses function and gradient values, J. Optim. Theory Appl., 28 (1979), pp. 455-480.
8. J. DENNIS AND R. SCHNABEL, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, 1983; reprinted as Classics Appl. Math. 16, SIAM, Philadelphia, PA, 1996.
9. J. DENNIS AND R. SCHNABEL, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, 1983; reprinted as Classics Appl. Math. 16, SIAM, Philadelphia, PA, 1996.
10. J. DONGARRA, J. DUCROZ, S. HAMMERLING, AND R. HANSON, An extended set of Fortran basic linear algebra solvers, ACM Trans. Math. Software, 14 (1989), pp. 1-17.
11. P. GlLL, G. GOLUB, W. MURRAY, AND M. SAUNDERS, Factorized variable metric methods for unconstrained optimization, Math. Comp., 30 (1976), pp. 796-811.
12. D. LlU AND J. NOCEDAL, On the limited memory BFGS method for large scale optimization, Math. Programming, 45 (1989), pp. 503-528
13. J. MORÉ AND D. SORENSEN, Computing a trust region step, SIAM J. Sci. Stat. Comput., 4 (1983), pp. 553-572.
14. L. NAZARETH, The method of successive affine reduction for nonlinear minimization, Math. Programming, 35 (1986), pp. 97-109.
15. J. NOCEDAL, Updating quasi-Newton matrices with limited storage, Math. Comp., 35 (1980), pp. 773-782.
16. S. OREN AND E. SPEDICATO, Optimal conditioning of self-scaling and variable metric algorithms, Math Programming, 10 (1976), pp. 70-90.
17. D. SHANNO AND K. PHUA, Matrix conditioning and nonlinear optimization, Math. Programming, 14 (1978), pp. 145-160.