Skip to main content
Log in

Testing Parallel Variable Transformation

  • Published:
Computational Optimization and Applications Aims and scope Submit manuscript

Abstract

This paper studies performance of the parallel variable transformation (PVT) algorithm for unconstrained nonlinear optimization through numerical experiments on a Fujitsu VPP500, one of the most up-to-date vector parallel computers. Special attention is paid to a particular form of the PVT algorithm that is regarded as a generalization of the block Jacobi algorithm that allows overlapping of variables among processors. Implementation strategies on the VPP500 are described in detail and results of numerical experiments are reported.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D.P. Bertsekas and J.N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods, Prentice-Hall: Englewood Cliffs, N.J., 1989.

    Google Scholar 

  2. I. Bongartz, A.R. Conn, N. Gould and Ph.L. Toint, “CUTE: Constrained and unconstrained testing environment,” Research Report RC18860, IBM T.J. Watson Research Center, Yorktown, 1993.

    Google Scholar 

  3. A.R. Conn, N.I.M. Gould, M. Lescrenier and Ph.L. Toint, “Performance of a multifrontal scheme for partially separable optimization,” Report 88/4, Department of Mathematics, Facultés Universitaires Notre-Dame de la Paix, Namur, Belgium, 1988.

    Google Scholar 

  4. M.C. Ferris and O.L. Mangasarian, “Parallel variable distribution,” SIAM J. on Optimization, vol. 4, pp. 102-126, 1994.

    Google Scholar 

  5. Fujitsu Limited, Handbook for UXP/V VPP Programming (in Japanese), Fujitsu Limited: Tokyo, 1997.

    Google Scholar 

  6. M. Fukushima, “Parallel variable transformation in unconstrained optimization,” SIAM J. on Optimization, vol. 8, pp. 658-672, 1998.

    Google Scholar 

  7. S.-P. Han, “Optimization by updated conjugate subspaces,” in D.F. Griffiths and G.A. Watson (eds.), Numerical Analysis: Pitman Research Notes in Mathematics Series 140, Longman Scientific & Technical: Burnt Mill, England, 1986, pp. 82-97.

    Google Scholar 

  8. A. Hirano, “An introduction to the VPP for MSP users (in Japanese),” The Bulletin of Kyoto University Data Processing Center, vol. 28, pp. 63-75, 1995.

    Google Scholar 

  9. A. Hirano, “An introduction to parallel programming (in Japanese),” The Bulletin of Kyoto University Data Processing Center, vol. 28, pp. 116-136, 1995.

    Google Scholar 

  10. O.L. Mangasarian, “Parallel gradient distribution in unconstrained optimization,” SIAM J. on Control and Optimization, vol. 33, pp. 1916-1925, 1995.

    Google Scholar 

  11. J.J. Moré, B.S. Garbow and K.E. Hillstrom, “Testing unconstrained optimization software,” ACM Trans. Math. Software, vol. 7, pp. 17-41, 1981.

    Google Scholar 

  12. S.G. Nash, “Newton-type minimization via the Lanczos method,” SIAM J. on Numerical Analysis, vol. 21, pp.770-788, 1984.

    Google Scholar 

  13. S.S. Oren, “Self-scaling variable metric (SSVM) algorithms Part II: Implementation and experiments,” Management Science, vol. 20, pp. 863-874, 1974.

    Google Scholar 

  14. J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press: New York, N.Y., 1970.

    Google Scholar 

  15. M.V. Solodov, “New inexact parallel variable distribution algorithms,” Computational Optimization and Applications, vol. 7, pp. 165-182, 1997.

    Google Scholar 

  16. Ph.L. Toint, “Test problems for partially separable optimization and results for the routine PSPMIN,” Report 83/4, Department of Mathematics, Facultés Universitaires Notre-Dame de la Paix, Namur, Belgium, 1983.

    Google Scholar 

  17. E. Yamakawa and M. Fukushima, “A block-parallel conjugate gradient method for separable quadratic programming problems,” J. Operations Research Society of Japan, vol. 39, pp. 407-427, 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yamakawa, E., Fukushima, M. Testing Parallel Variable Transformation. Computational Optimization and Applications 13, 253–274 (1999). https://doi.org/10.1023/A:1008629511432

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008629511432

Navigation