multi-stage accelerated stochastic approximation (AC-SA) for stochast…

…ic optimization

AC-SA/multi_stage.m

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+fprintf('     \n');
+fprintf('*** Running Multi-stage AC-SA\n');
+% Estimating sigma
+variance_estimate = var(x_initial')+ mean(x_initial').^2;
+sigma = 2*st*sqrt(max(variance_estimate));
+for j = 1 : Run_times
+    tic
+    p = initial_solution;
+    ek = (1/N)*(y_initial - x_initial*p)'*(y_initial - x_initial*p) + lamda*norm(p)^2;
+    k = 1;
+    N_sum = 0;
+    index = 0;
+    %step1
+    while N_sum < N_iter
+        Nk = ceil(max(sqrt(L/mu) , 128*(M^2+sigma^2)/(3* mu*ek/2)));
+        gamma = max(2*L, sqrt(((M^2+sigma^2)*mu/(3*ek))*(Nk+1)*(Nk+2)*Nk));
+        if Nk > (N_iter - N_sum)
+            Nk = N_iter - N_sum;
+        end
+        Rk = 1e+15;
+        AC_SA_sub;
+        ek = ek/2;
+        N_sum = N_sum + Nk;
+        k = k+1;
+    end
+    final_solution = p';
+    objective_computation;
+end
+Computing_Data;
+% file_name = [filename,'.txt'];
+% frep=fopen(file_name,'a');
+frep=fopen('Results.txt','a');
+count_alg = count_alg +1;
+if count_alg == 1
+    fprintf(frep,'     \n');
+    fprintf(frep,'********** Data: %s , rho: %6.5g\n',filename, lamda);
+end
+fprintf(frep,'     \n');
+fprintf(frep,'*** Running Multi-stage AC-SA\n');
+fprintf(frep,'     \n');
+fprintf(frep,'       Runtime:% 4.2f     Final objective value:% 6.2f\n', final_data);
+fclose(frep);
+
+
+