Long vectors for quasi-Newton updates |
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Authors: | Albert G Buckley |
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Institution: | (1) Department of Mathematics, Statistics and Computing Science, Dalhousie University, B3H 3J5 Halifax, N.S., Canada |
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Abstract: | 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
n ×n
of minimum Frobenius norm are converted to equivalent problems, using vector representations in ℝ
n2
and ℝ
n(n+1)/2 of these matrices, and then solvingl
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. |
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Keywords: | Quasi-Newton updates long vectors direct products l 2-minimization |
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