Preconditioning reduced matrices

SIAM Journal on Matrix Analysis and Applications

Volumn 17, Issue 1, 1996, Pages 47-68

  Nash, Stephen G ^a   Sofer, Ariela ^a  

^a George Mason University   (United States)

Author keywords

Conjugate gradient method; Nonlinear programming; Preconditioning; Reduced Hessian

Indexed keywords

EID: 0030531469     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479893245371     Document Type: Article

References (14)

1. C.H. BISCHOF, Incremental condition estimation, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 312-322.
2. R.S. DEMBO AND T. STEIHAUG, Truncated-Newton algorithms for large-scale unconstrained optimization, Math. Prog., 26 (1983), pp. 190-212.
3. R. FLETCHER, Practical Methods of Optimization, Volume 2 : Constrained Optimization, Wiley, New York, 1981.
4. P.E. GILL AND W. MURRAY, The numerical solution of a problem in the calculus of variations, in Recent Mathematical Developments in Control, D.J. Bell, ed., Academic Press, London, 1979, pp. 97-122.
5. P.E. GILL, W. MURRAY, D.B. PONCELEÓN, AND M.A. SAUNDERS, Preconditioners for indefinite systems arising in optimization, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 292-311.
6. P.E. GILL, W. MURRAY, AND M.H. WRIGHT, Practical Optimization, Academic Press, New York, 1981.
7. G.H. GOLUB AND C. VAN LOAN, Matrix Computations, 2nd ed., The Johns Hopkins University Press, Baltimore, 1989.
8. M.R. HESTENES, Conjugate-Direction Methods in Optimization, Springer-Verlag, New York, 1980.
9. D.K. KAHANER, C. MOLER, AND S.G. NASH, Numerical Methods and Software, Prentice-Hall, Englewood Cliffs, NJ, 1989.
10. S.G. NASH, Newton-like minimization via the Lanczos method, SIAM J. Numer. Anal., 21 (1984), pp. 770-788.
11. _, Preconditioning of truncated-Newton methods, SIAM J. Sci. Statist. Comput., 6 (1985), pp. 599-616.
12. S.G. NASH AND J. NOCEDAL, A numerical study of the limited memory BFGS method and the truncated-Newton method for large scale optimization, SIAM J. Optim., 1 (1991), pp. 358-372.
13. S.G. NASH AND A. SOFER, A barrier method for large-scale constrained optimization, ORSA J. Comput., 5 (1993), pp. 40-53.
14. T. RUSTEN AND R. WINTHER, A preconditioned iterative method for saddlepoint problems, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 887-904.