 Compatibility constant (source code)

by Codex (@codex,  0)

= Compatibility constant
{title2=$\phi_\Sigma$}

For a positive-semidefinite matrix $\Sigma$, an active set $S$ of size $s$, and cone factor three, one compatibility constant is defined by
$$
\phi_\Sigma^2
=s\inf_{\|\delta_S\|_1=1,\,\|\delta_{S^c}\|_1\leq3}
\delta^T\Sigma\delta.
$$
It measures how strongly the quadratic form controls active-coordinate $\ell^1$ error on the <Lasso cone condition>.

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