Algorithm 2. (modified G-PPA)

Step 1. Let $\eta \ge 1$ , $x_0\in X$ , $\zeta \mathrm{<mo>\; >\; </mo>0}$ and put $k\mathrm{<mo>\; :\; </mo>\; <mo>\; =\; </mo>0}$ .

Step 2. If $0\in T\left({\zeta }_k\mathrm{,}{x}_k\right)$ , then stop; otherwise, go to Step 3.

Step 3. Put $\left\{{\zeta }_k\right\}\subseteq \left(\mathrm{0,}\zeta \right)$ and if $0\notin T\left({\zeta }_k\mathrm{,}{x}_k\right)$ , choose $t_k$ such that $t_k\in T\left({\zeta }_k\mathrm{,}{x}_k\right)$ and $\Vert t_k\Vert \le \eta \mathrm{<mi>\; </mi>}\text{dist}\left(0,T\left({\zeta }_k,x_k\right)\right).$

Step 4. Write $x_{k+1}\mathrm{<mo>\; :\; </mo>\; <mo>\; =\; </mo>}{x}_k+t_k$ .

Step 5. Set $k$ by $k+1$ and go to Step 2.