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.
Similar content being viewed by others
References
D.P. Bertsekas and J.N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods, Prentice-Hall: Englewood Cliffs, N.J., 1989.
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.
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.
M.C. Ferris and O.L. Mangasarian, “Parallel variable distribution,” SIAM J. on Optimization, vol. 4, pp. 102-126, 1994.
Fujitsu Limited, Handbook for UXP/V VPP Programming (in Japanese), Fujitsu Limited: Tokyo, 1997.
M. Fukushima, “Parallel variable transformation in unconstrained optimization,” SIAM J. on Optimization, vol. 8, pp. 658-672, 1998.
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.
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.
A. Hirano, “An introduction to parallel programming (in Japanese),” The Bulletin of Kyoto University Data Processing Center, vol. 28, pp. 116-136, 1995.
O.L. Mangasarian, “Parallel gradient distribution in unconstrained optimization,” SIAM J. on Control and Optimization, vol. 33, pp. 1916-1925, 1995.
J.J. Moré, B.S. Garbow and K.E. Hillstrom, “Testing unconstrained optimization software,” ACM Trans. Math. Software, vol. 7, pp. 17-41, 1981.
S.G. Nash, “Newton-type minimization via the Lanczos method,” SIAM J. on Numerical Analysis, vol. 21, pp.770-788, 1984.
S.S. Oren, “Self-scaling variable metric (SSVM) algorithms Part II: Implementation and experiments,” Management Science, vol. 20, pp. 863-874, 1974.
J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press: New York, N.Y., 1970.
M.V. Solodov, “New inexact parallel variable distribution algorithms,” Computational Optimization and Applications, vol. 7, pp. 165-182, 1997.
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.
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.
Author information
Authors and Affiliations
Rights 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
Issue Date:
DOI: https://doi.org/10.1023/A:1008629511432