A Generalized Robust Minimization Framework for Low-Rank Matrix Recovery

Algorithm 2

Set 0<𝜂<1,𝜆,𝜈,𝜏,𝐽. Initialize 𝑗=1,𝐴^0/−1,𝐵^0/−1,Λ⁰,Γ⁰,𝜈⁰.

while Residual error = (Λ^𝑗−𝐴^𝑗+1)+(𝐵^𝑗+1−Γ^𝑗)_𝐿2√2max1,Λ^𝑗2_𝐿2+Γ^𝑗2_𝐿2>𝜏

 Λ^𝑗=𝐴^𝑗+𝑡_𝑗−1−1𝑡_𝑗𝐴^𝑗−𝐴^𝑗−1,Γ^𝑗=𝐵^𝑗+𝑡_𝑗−1−1𝑡_𝑗𝐵^𝑗−𝐵^𝑗−1;

 𝐺^𝑗_Λ=Λ^𝑗−12Λ^𝑗+Γ^𝑗−𝐶,𝐺^𝑗_Γ=Γ^𝑗−12Λ^𝑗+Γ^𝑗−𝐶,

 𝐴^𝑗+1=argmin_𝐴𝑄𝐴,𝐵^𝑗,Λ^𝑗,Γ^𝑗,𝜈^𝑗;

 𝐵^𝑗+1=argmin_𝐵𝑄𝐴^𝑗+1,𝐵,Λ^𝑗,Γ^𝑗,𝜈^𝑗;

 𝜈^𝑗+1=max𝜂𝜈^𝑗,𝜈;

 𝑗=𝑗+1;

 if 𝑗>𝐽  break; end

end