| Title:
|
A note on direct methods for approximations of sparse Hessian matrices (English) |
| Author:
|
Tůma, Miroslav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
3 |
| Year:
|
1988 |
| Pages:
|
171-176 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
Necessity of computing large sparse Hessian matrices gave birth to many methods for their effective approximation by differences of gradients. We adopt the so-called direct methods for this problem that we faced when developing programs for nonlinear optimization. A new approach used in the frame of symmetric sequential coloring is described. Numerical results illustrate the differences between this method and the popular Powell-Toint method. (English) |
| Keyword:
|
large sparse optimization |
| Keyword:
|
numerical examples |
| Keyword:
|
sparse Hessian matrices |
| Keyword:
|
finite-differences |
| Keyword:
|
graph-coloring |
| Keyword:
|
ordering scheme |
| Keyword:
|
coloring scheme |
| MSC:
|
65D15 |
| MSC:
|
65D25 |
| MSC:
|
65F20 |
| MSC:
|
65H10 |
| MSC:
|
65K05 |
| MSC:
|
90C30 |
| idZBL:
|
Zbl 0658.65058 |
| idMR:
|
MR0944781 |
| DOI:
|
10.21136/AM.1988.104300 |
| . |
| Date available:
|
2008-05-20T18:34:30Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104300 |
| . |
| Reference:
|
[1] T. F. Coleman J. J. Moré: Estimation of Sparse Hessian Matrices and Graph Coloring Problems.Math. Prog. 28 (1984), 243-270. MR 0736293, 10.1007/BF02612334 |
| Reference:
|
[2] G. C. Everstine: A Comparison of Three Resequencing Algorithms for the Reduction of Matrix Profile and Wavefront.International Journal on Numerical Methods in Engineering 14 (1979), 837-853. Zbl 0401.73082, 10.1002/nme.1620140606 |
| Reference:
|
[3] A. George J. W. H. Liu: Computer Solution of Large Sparse Positive Definite Systems.Prentice-Hall, Inc. Englewood Cliffs. N. J. 07632, 1981. MR 0646786 |
| Reference:
|
[4] P. Hanzálek J. Hřebíček J. Kučera: A Conversational Program System for Mathematical Optimization.Computer Physics Communications 41 (1986), 403 - 408. 10.1016/0010-4655(86)90080-9 |
| Reference:
|
[5] D. M. Matula L. L. Beck: Smallest-last Ordering and Clustering and Graph Coloring Algorithms.JACM 30 (1983), 417-427. MR 0709826, 10.1145/2402.322385 |
| Reference:
|
[6] S. T. McCormick: Optimal Approximation of Sparse Hessians and its Equivalence to a Graph Coloring Problem.Math. Prog. 26 (1983), 153-171. Zbl 0507.65027, MR 0700644, 10.1007/BF02592052 |
| Reference:
|
[7] M. J. D. Powell, Ph. L. Toint: On the Estimation of Sparse Hessian Matrices.SIAM on Num. Anal. 16 (1979), 1060-1074. Zbl 0426.65025, MR 0551326, 10.1137/0716078 |
| Reference:
|
[8] M. N. Thapa: Optimization of Unconstrained Functions with Sparse Hessian Matrices: Newton-type Methods.Math. Prog. 19 (1984), 156-186. Zbl 0538.49023, MR 0745406 |
| Reference:
|
[9] O. C. Zienkiewicz: The Finite Element Method.McGraw Hill, London, 1977. Zbl 0435.73072 |
| . |
