Algorithm 8 Gradient update for α in the direction v
1:	for τ = 0 to k do
2:	$\alpha \left(\frac{\tau }{k}\right)={\chi }_1\left(\alpha \left(\frac{\tau }{k}\right);-v\left(\frac{\tau }{k}\right)\right)$
3:	Project $\alpha \left(\frac{\tau }{k}\right)$ into using Algorithm 1
4:	end for