| Title:
|
Computational experience with improved variable metric methods for unconstrained minimization (English) |
| Author:
|
Lukšan, Ladislav |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
26 |
| Issue:
|
5 |
| Year:
|
1990 |
| Pages:
|
415-431 |
| . |
| Category:
|
math |
| . |
| MSC:
|
65K05 |
| MSC:
|
90C30 |
| idZBL:
|
Zbl 0716.65055 |
| idMR:
|
MR1079679 |
| . |
| Date available:
|
2009-09-24T18:21:02Z |
| Last updated:
|
2012-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124597 |
| . |
| Reference:
|
[1] M. C. Biggs: Minimization algorithms making use of nonquadratic properties of the objective function.J. Inst. Maths. Applies. 8 (1971), 315-327. |
| Reference:
|
[2] C. G. Broyden: The convergence of a class of double rank minimization algorithms, Part 1: general considerations. Part 2: the new algorithm.J. Inst. Maths. Applies. 6 (1970), 76 - 90, 222-231. MR 0433870 |
| Reference:
|
[3] R. H. Byrd J. Nocedal, Y. X. Yuan: Global convergence of a class of quasi-Newton methods on convex problems.SIAM J. Numer. Anal. 24 (1987), 1171-1190. MR 0909072 |
| Reference:
|
[4] A. R. Conn N. I. M. Gould, P. L. Toint: Testing a class of methods for solving minimzation problems with simple bounds on the variables.Math. Comp. 50 (1988), 399 - 430. MR 0929544 |
| Reference:
|
[5] L. C. W. Dixon: Variable metric algorithms: Necessary and sufficient conditions for identical behavior of nonquadratic functions.J. Optim. Theory Appl. 10 (1972), 34 - 40. MR 0309305 |
| Reference:
|
[6] R. Fletcher: A new approach to variable metric algorithms.Comput. J. 13 (1979), 317-322. |
| Reference:
|
[7] R. Fletcher: Practical Methods of Optimization.Vol. 1 Unconstrained Optimization. J. Wiley \& sons, New York 1980. Zbl 0439.93001, MR 0585160 |
| Reference:
|
[8] P. E. Gill W. Murray, M. Saunders: Methods for computing and modifying the LDV factors of a matrix.Math. Comp. 29 (1974), 1051-1077. MR 0388754 |
| Reference:
|
[9] D. Goldfarb: A family of variable metric algorithms derived by variational means.Math. Comp. 24(1970), 23-26. MR 0258249 |
| Reference:
|
[10] A. Griewank, P. L. Toint: Local convergence analysis for partitioned quasi-Newton updates.Numer. Math. 39 (1982), 429-448. Zbl 0505.65018, MR 0678746 |
| Reference:
|
[11] H. Kleinmichel: Quasi-Newton Verfahren vom Rang-Eins-Typ zur Lösung unrestringierter Minimierungsprobleme.Teil 1: Verfahren und grundlegende Eigenschaften. Teil 2: N-Schritt-quadratische Konvergenz fur Restart-Varianten. Numer. Math. 38 (1981), 219-228, 229-244. Zbl 0469.65039 |
| Reference:
|
[12] D. G. McDowell: Conditions of variable metric algorithms to be conjugate gradient algo- rithms.J. Optim. Theory Appl. 41 (1983), 439 - 450. MR 0728311 |
| Reference:
|
[13] J. J. More B. S. Garbow, K. E. Hillstrom: Testing unconstrained optimization software.ACM Trans. Math. Software 7 (1981), 17-41. MR 0607350 |
| Reference:
|
[14] S. S. Oren, and D. C. Luenberger: Self-scaling variable metric (SSVM) algorithms.Part 1: Criteria and sufficient conditions for-scaling a class of algorithms. Part 2: Implementation and experiments. Management Sci. 20 (1974), 845 - 862, 863-874. MR 0426427 |
| Reference:
|
[15] S. S. Oren, E. Spedicato: Optimal conditioning of self scaling variable metric algorithms.Math. Programming 10 (1976), 70 - 90. Zbl 0342.90045, MR 0401164 |
| Reference:
|
[16] M. R. Osborne, L. P. Sun: A New Approach to the Symmetric Rank-One Updating Algorithm.Rept. No. NMO/01, Australian National University School of Mathematics, December 1988. |
| Reference:
|
[17] D. F. Shanno: Conditioning of quasi-Newton methods for function minimization.Math. Comp. 24 (1970), 647-656. MR 0274029 |
| Reference:
|
[18] D. F. Shanno, K. J. Phua: Matrix conditioning and nonlinear optimization.Math. Programming 14 (1978), 144- 160. Zbl 0371.90109, MR 0474819 |
| Reference:
|
[19] E. Spedicato: A class of rank-one positive definite quasi-Newton updates for unconstrained minimization.Math. Operationsforsch. Statist., Ser. Optimization 14 (1983), 61 - 70. Zbl 0519.90075, MR 0694803 |
| Reference:
|
[20] J. Stoer: On the convergence rate of imperfect minimization algorithms in Broydeu's $\beta$-class.Math. Programming 9 (1975), 313-335. MR 0413491 |
| Reference:
|
[21] Y. Zhang, R. P. Tewarson: Least-change updates to Cholesky factors subject to the nonlinear quasi-Newton condition.IMA J. Numer. Anal. 7 (1987), 509-521. Zbl 0636.65061, MR 0968522 |
| Reference:
|
[22] Y. Zhang, R. P. Tewarson: Quasi-Newton algorithms with updates from the preconvex part of Broyden's family.IMA J. Numer. Anal. 8 (1988), 487-509. Zbl 0661.65061, MR 0975609 |
| . |
