Table 2 The framework of the MA

Step 0:

Choose $x_1\in C$, $r_1\in (0,+\mathrm{\infty })$, ${\alpha }_1\in [0,1)$. Set n: = 1.

Step 1:

Given $x_n\in C$. Choose $r_n\in (0,+\mathrm{\infty })$, ${\alpha }_n\in [0,1)$ and compute $x_{n+1}\in C$ as

  $\begin{array}{l}F(z_n,z)+\frac{1}{r_n}〈z-z_n,z_n-x_n〉\ge 0,\\ x_{n+1}={\alpha }_n{x}_n+(1-{\alpha }_n)z_n.\end{array}$