Algorithm 3.

Line search for RDA method

Input: c0, Ak−1, wk, Gk, ${\overline{G}}_{k-1}$, f (ck, wk), λ, αmax
Output: αk {Weight for k-th iteration.}
1:	$\stackrel{\sim }{\alpha }\leftarrow {\alpha }_{\mathit{max}}$ {αmax is the initial guess for the weight.}
2:	found ← false
3:	while not found do
4:	$\stackrel{\sim }{A}\leftarrow A_{k-1}+\stackrel{\sim }{\alpha }$
5:	$\stackrel{\sim }{G}\leftarrow \left(1-\frac{\stackrel{\sim }{\alpha }}{\stackrel{\sim }{A}}\right){\overline{G}}_{k-1}+\frac{\stackrel{\sim }{\alpha }}{\stackrel{\sim }{A}}{G}_k$
6:	$\stackrel{\sim }{\mu }\leftarrow \gamma \stackrel{\sim }{A}$ {Should be consistent with Alg. 2.}
7:	$\stackrel{\sim }{c}\leftarrow {\text{prox}}_{\lambda \stackrel{\sim }{\mu }ℛ}\left(c_0-\stackrel{\sim }{\mu }\stackrel{\sim }{G}\right)$
8:	if $f\left(\stackrel{\sim }{c},w_k\right)+\lambda ℛ\left(\stackrel{\sim }{c}\right)<f\left(c_k,w_k\right)+\lambda ℛ\left(c_k\right)$ then
9:	found ← true
10:	else
11:	$\stackrel{\sim }{\alpha }\leftarrow \stackrel{\sim }{\alpha }/2$
12:	end if
13:	end while
14:	${\alpha }_k\leftarrow \stackrel{\sim }{\alpha }$