Table A1.

Pseudo code for FISTA with line search.

FISTA with line search
Initialize x 0:= 0, v 0:= x 0, t 0> 0, 0 < r < 1
for k = 1,2,…,n, do
$t:=t_{k-1}/r$
Repeat
$\theta :=\left\{\begin{array}{cc}1& ifk=1\\ positiverootof{t}_{k-1}{\theta }^2=t{\theta }_{k-1}^2\left(1-\theta \right)& ifk>1\end{array}\right.$
$y:=\left(1-\mathrm{\theta }\right)x_{k-1}+\mathrm{\theta }{v}_{k-1}$
$x:={\mathbf{prox}}_{\mathit{tg}}\left(y-t\mathrm{\nabla }f(y)\right)$
break if $f\left(x\right)\le f\left(y\right)+<\mathrm{\nabla }f\left(y\right),x-y>+\frac{\mathbf{1}}{\mathbf{2}t}{\Vert x-y\Vert }_{\mathbf{2}}^{\mathbf{2}}$
$t:=\mathit{rt}$
$t_k:=t$
${\theta }_k:=\theta$ $x_k:=x$
$v_k:=x_k+\frac{1}{{\theta }_k}\left(x_k-x_{k-1}\right)$
end
return x