An H-form variant of the partitioned QN method

Authors:
M. B. Reed
Affiliations:
Department of Biological Sciences, Brunel University, Uxbridge UB8 3PH, UK
Venue:
Applied Numerical Mathematics
Year:
2003

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Remark on algorithm 630

ACM Transactions on Mathematical Software (TOMS)
Algorithm 711: BTN: software for parallel unconstrained optimization

ACM Transactions on Mathematical Software (TOMS)
Algorithm 630: BBVSCG–a variable-storage algorithm for function minimization

ACM Transactions on Mathematical Software (TOMS)

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Abstract

This paper introduces a technique for transforming partitioned quasi-Newton algorithms into H-form algorithms. The resulting algorithms have essentially the same space requirements as the standard partitioned QN method, but involve only a global matrix-vector multiplication (rather than a global solution by conjugate gradients) at each iteration. Results demonstrate that the method, which is highly suitable for parallelization, is competitive with other quasi-Newton methods in minimizing partially separable polynomial functions of large dimension.