Multi-directional parallel algorithms for unconstrained optimization

Optimization

Volumn 38, Issue 2, 1996, Pages 107-125

  Phua, Paul Kang Hoh ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

BFGS up date; Nonlinear optimization; Parallel optimization; Quasi Newton; SR1 update

Indexed keywords

EID: 0039926771     PISSN: 02331934     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331939608844242     Document Type: Article

References (18)

1. Biggs, M. C. (1973) A note on minimization algorithms which make use of non-quadratic properties of the objective function, J. lnst. Maths Applics, 12, 337-338
2. Brent, R. P. (1973) Algorithms for Minimization without Derivatives, Prentice-Hall, Inc., Englewood Cliffs, New Jersey,
3. Broyden, C. G. (1967) Quasi-Newton methods and their application to function minimization, Math. Comp., 21, 368-381
4. Byrd, R. H. Schnabel, R. B. and Shultz, G. A. (1988) Parallel quasi-Newton methods for unconstrained optimization, Mathematical Programming, 42, 273-306
5. Golub, H. G. and van Loan, C. (1989) Matrix Computation, 2nd ed., Johns Hopkins University Press, Baltimore, MD,
6. Lootsma, F. A. and Ragsdell, K. M. (1988) State-of-the-art in parallel nonlinear optimization, Parallel Computing, 6, 133-155
7. More, J. J. Garbow, B. S. and Hillstrom, K. E. (1981) Testing unconstrained optimization software, ACM Transactions on Mathematical Software, 7, 17-41
8. Oren, S. S. (1974) Self-scaling variable metric algorithm Part II, Management Science, 20, 863-874
9. Phua, P. K. H. (1993) Switching algorithms for quasi-Newton methods, FSU-SCRI-93T-151, Supercomputer Computations Research Institute, Florida State University, December 28, pp
10. Phua, P. K. H. and Chew, S. B. (1992) Symmetric rank-one update and quasi-Newton methods, in: P. K. H. Phua et al., eds., Optimization Techniques and Applications, World Scientific Singapore 52-63
11. Schnabel, R. B. (1987) Concurrent function evaluation in local and global optimization, Computer Methods in Applied Mechanics and Engineering, 64, 537-552
12. Shanno, D. F. (1970) Conditioning of quasi-Newton methods for function minimization, Math. Comp., 24, 647-656
13. Shanno, D. F. and Phua, P. K. H. (1980) Remark on Algorithm 500-a variable method subroutine for unconstrained nonlinear optimization, ACM Trans. Math. Software, 6, 618-622
14. Straeter, T. A. (1973) A parallel variable metric optimization algorithm. NASA Technical Note, NASA TN D-7329, Langley Research Center, Hampton, VA 23665,
15. Toint, Ph. L. (1978) Some numerical results using a sparse matrix updating formula in unconstrained optimization, Mathematics of Computation, 32, 839-852
16. van Laarhoven, P. J. M. (1985) Parallel variable metric algorithms for unconstrained optimization, Mathematical Programming, 33, 68-81
17. Wilkinson, J. H. (1965) The algebraic eigenvalue problem, clarendon Press, Oxford, England
18. Yuan, Y. (1991) A modified BFGS algorithm for unconstrained optimization, optimization, IMA Journal of Numerical Analysis, 11, 325-332