Long vectors for quasi-Newton updates

This work concerns the derivation of formulae for updating quasi-Newton matrices used in algorithms for computing approximate minima of smooth unconstrained functions. The paper concentrates strictly on the techniques used to derive update formulae. It demonstrates a technique in which problems of f...

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Bibliographic Details
Published in:Mathematical programming 1986, Vol.36 (3), p.256-275
Main Author: BUCKLEY, A. G
Format: Article
Language:English
Subjects:
Applied sciences
Exact sciences and technology
Mathematical programming
Operational research and scientific management
Operational research. Management science
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Summary:This work concerns the derivation of formulae for updating quasi-Newton matrices used in algorithms for computing approximate minima of smooth unconstrained functions. The paper concentrates strictly on the techniques used to derive update formulae. It demonstrates a technique in which problems of finding matrices in R super(nxn) of minimum Frobenius norm are converted to equivalent problems, using vector representations in R super(n2) and R super(n(n+1)/2) of these matrices, and then solving l sub(2)-minimization problems. These problems are more directly dealt with, and indeed, the paper demonstrates how this technique may be used to handle weighted sparse updates.
ISSN:0025-5610
1436-4646
DOI:10.1007/BF02592061