TestSBM.m

%First experiment: small-scale problem.
%Goal: Show that the primal formulation is better when Z^* is 'low' rank 
%Instance: rank(X^*) = 97 or rank(Z^*) = 3

% The penalty parameter is chosen by the fact that we already know the optimal solution 
% Penal term is chosen as tr(X^*)*2+2 and tr(Z^*)*2+2

%Authors: Feng-Yi Liao & Yang Zheng
%         SOC Lab @UC San Diego
 
clc;clear;
addpath('packages\SBM-Primal');
addpath('packages\SBM-Dual');
addpath('packages\General');
filename = "n100m100dr3";
load("examples\randomSDPs\"+filename+".mat");

opts.n              = K_sdp.s; 
opts.m              = height(At_sdp); 
opts.epislon        = 10^-20; 

opts.beta           = 0.25; 
opts.mu             = 0.5; 
opts.alpha          = 50; %does not matter for adaptive case 

%%%%%%%%%% [Primal] %%%%%%%%%%
%We do not count the first iteration for SBMP

    opts.Maxiter     = 201;
    opts.rho         = Optimal.TrZ*2+2;
    opts.MaxCols     = 2;
    opts.EvecPast    = 1;
    opts.EvecCurrent = 1;
    opts.solver      = "primal";
    Out_Primal_1_1   = SBM(At_sdp,b_sdp,c_sdp,K_sdp,opts);
 
    opts.Maxiter     = 201;
    opts.rho         = Optimal.TrZ*2+2;
    opts.MaxCols     = 3;
    opts.EvecPast    = 2;
    opts.EvecCurrent = 1;
    opts.solver      = "primal";
    Out_Primal_2_1   = SBM(At_sdp,b_sdp,c_sdp,K_sdp,opts);

    opts.Maxiter     = 201;
    opts.rho         = Optimal.TrZ*2+2;
    opts.MaxCols     = 4;
    opts.EvecPast    = 3;
    opts.EvecCurrent = 1;
    opts.solver      = "primal";
    Out_Primal_3_1   = SBM(At_sdp,b_sdp,c_sdp,K_sdp,opts);

    opts.Maxiter     = 201;
    opts.rho         = Optimal.TrZ*2+2;
    opts.MaxCols     = 2;
    opts.EvecPast    = 0;
    opts.EvecCurrent = 2;
    opts.solver      = "primal";
    Out_Primal_0_2   = SBM(At_sdp,b_sdp,c_sdp,K_sdp,opts);
  
    opts.Maxiter     = 201;
    opts.rho         = Optimal.TrZ*2+2;
    opts.MaxCols     = 3;
    opts.EvecPast    = 0;
    opts.EvecCurrent = 3;
    opts.solver      = "primal";
    Out_Primal_0_3   = SBM(At_sdp,b_sdp,c_sdp,K_sdp,opts);

    opts.Maxiter     = 201;
    opts.rho         = Optimal.TrZ*2+2;
    opts.MaxCols     = 4;
    opts.EvecPast    = 0;
    opts.EvecCurrent = 4;
    opts.solver      = "primal";
    Out_Primal_0_4   = SBM(At_sdp,b_sdp,c_sdp,K_sdp,opts);
% 
% 
% %%%%%%%%%% [Dual] %%%%%%%%%%
%     
% 
    opts.Maxiter     = 200;
    opts.rho         = Optimal.TrX*2+2;
    opts.MaxCols     = 2;
    opts.EvecPast    = 0;
    opts.EvecCurrent = 2;
    opts.solver      = "dual";
    Out_Dual_0_2     = SBM(At_sdp,b_sdp,c_sdp,K_sdp,opts);
      
    opts.Maxiter     = 200;
    opts.rho         = Optimal.TrX*2+2;
    opts.MaxCols     = 3;
    opts.EvecPast    = 0;
    opts.EvecCurrent = 3;
    opts.solver      = "dual";
    Out_Dual_0_3     = SBM(At_sdp,b_sdp,c_sdp,K_sdp,opts);
    
    opts.Maxiter     = 200;
    opts.rho         = Optimal.TrX*2+2;
    opts.MaxCols     = 4;
    opts.EvecPast    = 0;
    opts.EvecCurrent = 4;
    opts.solver      = "dual";
    Out_Dual_0_4     = SBM(At_sdp,b_sdp,c_sdp,K_sdp,opts);
% 
% save("results_rdSDPs_new\"+filename+"_result.mat",'Out_Primal_1_1','Out_Primal_2_1','Out_Primal_3_1','Out_Primal_0_2','Out_Primal_0_3','Out_Primal_0_4',...
%      'Out_Dual_0_2','Out_Dual_0_3','Out_Dual_0_4');