Algorithm 1 Find optimal ${\theta }_a^{*}$
1:	Input:${\lambda }_a$, ${\theta }_a^{min}=0$ and ${\theta }_a^{max}=1$, precision ${\epsilon }_{\theta }$
2:	Output:${\theta }_a^{*}$
3:	Compute $f_1({\theta }_a^{min})$, $f_1({\theta }_a^{max})$ by Equation (15).
4:	while$(f_1({\theta }_a^{min})f_1({\theta }_a^{max})<0\&\&({\theta }_a^{max}-{\theta }_a^{min})>{\epsilon }_{\theta })$do
5:	Set middle point ${\theta }_a^{\mathrm{mid}}=({\theta }_a^{min}+{\theta }_a^{max})/\phantom{({\theta }_a^{min}+{\theta }_a^{max})2}2$.
6:	Compute $f_1({\theta }_a^{\mathrm{mid}})$ by Equation (15).
7:	if $(f_1({\theta }_a^{\mathrm{mid}})>0)$ then
8:	${\theta }_a^{min}={\theta }_a^{\mathrm{mid}}$.
9:	else
10:	${\theta }_a^{max}={\theta }_a^{\mathrm{mid}}$.
11:	end if
12:	Compute $f_1({\theta }_a^{min})$, $f_1({\theta }_a^{max})$ by Equation (15).
13:	end while
14:	${\theta }_a^{*}=({\theta }_a^{min}+{\theta }_a^{max})/2$.
15:	END