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A parallel variable metric optimization algorithmAn algorithm, designed to exploit the parallel computing or vector streaming (pipeline) capabilities of computers is presented. When p is the degree of parallelism, then one cycle of the parallel variable metric algorithm is defined as follows: first, the function and its gradient are computed in parallel at p different values of the independent variable; then the metric is modified by p rank-one corrections; and finally, a single univariant minimization is carried out in the Newton-like direction. Several properties of this algorithm are established. The convergence of the iterates to the solution is proved for a quadratic functional on a real separable Hilbert space. For a finite-dimensional space the convergence is in one cycle when p equals the dimension of the space. Results of numerical experiments indicate that the new algorithm will exploit parallel or pipeline computing capabilities to effect faster convergence than serial techniques.
Document ID
19740004183
Acquisition Source
Legacy CDMS
Document Type
Other - NASA Technical Note (TN)
Authors
Straeter, T. A. (NASA Langley Research Center Hampton, VA, United States)
Date Acquired
September 3, 2013
Publication Date
December 1, 1973
Subject Category
Mathematics
Report/Patent Number
L-8986
NASA-TN-D-7329
Accession Number
74N12296
Funding Number(s)
PROJECT: RTOP 501-06-01-09
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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