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Guest
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Hi,
Barzilai and Borwein formulated 2 symmetric step-length formulas that
minimize
i) ||s_(k-1) - n * y_(k-1)||^2
ii) ||b * s_(k-1) - y_(k-1)||^2
with respect to n and b respectively, where,
1) s_k = w_(k+1) - w_k
2) y_k = g_(k+1) - g_k
3) g is gradient of a function
4) k is iteration number.
The step-lengths are used for iteration,
i) w_(k+1) = w_k - n_k * g_k
ii) w_(k+1) = w_k - b_k * g_k
respectively. The result they obtained were,
A) n_k = <s_(k-1), y_(k-1)> / < y_(k-1), y_(k-1)>
B) b_k = <s_(k-1), s_(k-1)> / < s_(k-1), y_(k-1)>
where <,> denotes inner dot product. Result (A) looks alright, but (B)
does not unless it is minimizing ||1/b * s_(k-1) - y_(k-1)||^2.
Any comment?
-Wumin |
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