Table 1.

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 $k=1,2,\dots$ do $t:=t_{k-1}/r$ Repeat $\theta :=\left\{\begin{array}{cc}1& \text{if}k=1\\ \text{positive root of}{t}_{k-1}{\theta }^2=t{\theta }_{k-1}^2\left(1-\theta \right)& \text{if}k>1\end{array}\right.$ $y:=\left(1-\theta \right)x_{k-1}+\theta v_{k-1}$ $x:=pro{x}_{\mathit{tg}}\left(y-t\mathrm{\nabla }f\left(y\right)\right)$ break if $f\left(x\right)\le f\left(y\right)+<\mathrm{\nabla }f\left(y\right),x-y>+\frac{1}{2t}{\Vert x-y\Vert }_2^2$ $t:=rt$ $t_k:=t$ ${\theta }_k:=\theta$ $x_k:=x$ $v_k:=x_k+\frac{1}{{\theta }_k}(x-x_k)$
End
Return $x$