Table 1 The framework of the EA

Step 0:

Choose $x_1\in C$, ${\lambda }_1\in [\lambda ,{\lambda }^{\prime }]$, ${\alpha }_1\in [0,1)$. Set n: = 1.

Step 1:

Given $x_n\in C$. Choose ${\lambda }_n\in [\lambda ,{\lambda }^{\prime }]$, ${\alpha }_n\in [0,1)$ and compute $x_{n+1}\in C$ as

  $\begin{array}{l}{y}_n={Proj}_C(x_n-{\lambda }_{n}A{x}_n),\\ x_{n+1}={\alpha }_n{x}_n+(1-{\alpha }_n){Proj}_C(x_n-{\lambda }_{n}A{y}_n).\end{array}$