Algorithm 1: POPFA Algorithm

Step 1: Choose ${\rho }_1>0,N>1,0<p\le 1$ and $k=1$. Step 2: Solve $({\mathit{u}}_1^k,{\mathit{u}}_2^k)$ to be a partial optimum of $$min{H}_p({\mathit{u}}_1,{\mathit{u}}_2,{\rho }_k)s.t.({\mathit{u}}_1,{\mathit{u}}_2)\in R^{n_1}\times R^{n_2}.$$ Step 3: If $({\mathit{u}}_1^k,{\mathit{u}}_2^k)$ is feasible to (BCP), stop and $({\mathit{u}}_1^k,{\mathit{u}}_2^k)$ is a partial optimum of (BCP). Otherwise, ${\rho }_{k+1}=N{\rho }_k,k=:k+1$ and go to Step 2.