A Generalized Robust Minimization Framework for Low-Rank Matrix Recovery

Algorithm 1

Set 1<𝜌<2,𝜆,𝜇,𝜀 and 𝐾. Initialize 𝑘=0,𝐵⁰,𝑋⁰,𝜇⁰

while Residual error = 𝐶−𝐴^𝑘+1−𝐵^𝑘+1_𝐿2max‖𝐶‖_∞/𝜆,‖𝐶‖₂>𝜀

 𝐴^𝑘+1=argmin_𝐴𝐿(𝐴,𝐵^𝑘,𝑋^𝑘,𝜇^𝑘);

 𝐵^𝑘+1=argmin_𝐵𝐿(𝐴^𝑘+1,𝐵,𝑋^𝑘,𝜇^𝑘);

 𝑋^𝑘+1=𝑋^𝑘+𝜇^𝑘(𝐶−𝐴^𝑘+1−𝐵^𝑘+1);

 𝜇^𝑘+1=min{𝜌𝜇^𝑘,𝜇};

 𝑘=𝑘+1;

 if  𝑘>𝐾  break; end

end