Item Details

A Parallel Variable Metric Optimization Algorithm

by Terry A. Straeter
Format
Book; Government Document; Online; EBook
Published
Washington, D.C. : National Aeronautics and Space Administration ; [Springfield, Va. : For sale by the National Technical Information Service], 1973.
Language
English
Series
NASA Technical Note
Summary
An 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.
Description
21 p. : ill. ; 27 cm.
Mode of access: Internet.
Notes
  • Prepared at Langley Research Center.
  • Cover title.
  • Bibliography: p. 20-21.
Series Statement
NASA technical note ; NASA TN D-7329
Logo for No Copyright - United StatesNo Copyright - United States
Technical Details

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    a| Straeter, Terry A. q| (Terry Anthony), d| 1942-
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    a| A parallel variable metric optimization algorithm c| by Terry A. Straeter.
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    a| Washington, D.C. : b| National Aeronautics and Space Administration ; a| [Springfield, Va. : b| For sale by the National Technical Information Service], c| 1973.
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    a| 21 p. : b| ill. ; c| 27 cm.
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    a| NASA technical note ; v| NASA TN D-7329
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    a| Prepared at Langley Research Center.
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    a| Cover title.
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    a| Bibliography: p. 20-21.
    520
      
      
    a| An 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.
    538
      
      
    a| Mode of access: Internet.
    650
      
    0
    a| Algorithms.
    650
      
    0
    a| Parallel processing (Electronic computers)
    650
      
    0
    a| Mathematical optimization.
    650
      
    0
    a| Numerical analysis x| Computer programs.
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    1
      
    a| United States. b| National Aeronautics and Space Administration.
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    a| Langley Research Center.
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    b| UIU c| UIUC d| 20141113 s| google u| uiug.30112106885491 y| 1973 r| pd q| bib

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