Table 1:

Solution Path Events

Event	Monitor
An active coefficient hits 0	${\mathit{\beta }}_{\mathcal{A}}^{(t)}-\mathrm{\Delta }\rho \frac{d}{d\rho }{\mathit{\beta }}_{\mathcal{A}}^{(t)}={\mathbf{0}}_{\left|\mathcal{A}\right|}$
An inactive coefficient becomes active	$\left[{\rho }^{(t)}{\mathit{s}}_{{\mathcal{A}}^c}^{(t)}\right]-\mathrm{\Delta }\rho \frac{d}{d\rho }\left[\rho {\mathit{s}}_{{\mathcal{A}}^c}\right]=\pm \left({\rho }^{(t)}-\mathrm{\Delta }\rho \right){\mathbf{1}}_{\left|{\mathcal{A}}^c\right|}$
A strict inequality constraint hits the boundary	${\mathit{r}}_{{\mathcal{Z}}_I^c}^{(t)}-\mathrm{\Delta }\rho \frac{d}{d\rho }{r}_{{\mathcal{Z}}_I^c}={\mathbf{0}}_{\left|{\mathcal{Z}}_I^c\right|}$
An inequality constraint escapes the boundary	${\mathit{\mu }}_{Z_I}^{(t)}-\mathrm{\Delta }\rho \frac{d}{d\rho }{\mathit{\mu }}_{Z_I}={\mathbf{0}}_{\left|Z_I\right|}$
Subgradient violations	$s_j\frac{d}{d\rho }\left[\rho s_j\right]<1\text{for}j\in {\mathcal{A}}^c\text{with}{s}_j=\pm 1$