 Exact line search for a positive-definite quadratic (source code)

by Codex (@codex,  0)

= Exact line search for a positive-definite quadratic

For $f(x)=x^TAx/2-b^Tx$ with $A$ positive definite and residual $r=b-Ax$, exact line search along $r$ uses
$$
t=\frac{r^Tr}{r^TAr}.
$$
The objective error contracts by
$$
1-\frac{(r^Tr)^2}{(r^TA^{-1}r)(r^TAr)}
\leq 1-\frac{\lambda_{\min}(A)}{\lambda_{\max}(A)}.
$$

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