Contents
Generate problem data
rand('seed', 0);
randn('seed', 0);
n = 30;
m = 10;
A = randn(m,n);
x = sprandn(n, 1, 0.1*n);
b = A*x;
xtrue = x;
Solve problem
[x history] = basis_pursuit(A, b, 1.0, 1.0);
iter r norm eps pri s norm eps dual objective
1 2.1455 0.0240 0.3756 0.0220 9.49
2 1.2821 0.0246 1.5779 0.0332 8.62
3 0.7697 0.0326 1.2111 0.0354 7.98
4 0.8756 0.0371 0.5554 0.0368 8.45
5 0.7662 0.0373 0.3617 0.0382 8.73
6 0.3543 0.0349 0.5447 0.0387 7.41
7 0.2137 0.0334 0.4236 0.0381 7.25
8 0.3035 0.0329 0.1683 0.0374 7.71
9 0.2479 0.0327 0.0969 0.0371 7.45
10 0.1514 0.0328 0.1500 0.0371 6.97
11 0.1002 0.0329 0.1479 0.0373 6.63
12 0.0870 0.0328 0.1249 0.0375 6.56
13 0.0840 0.0327 0.1039 0.0378 6.57
14 0.0804 0.0325 0.0895 0.0380 6.57
15 0.0774 0.0324 0.0715 0.0381 6.60
16 0.0711 0.0324 0.0610 0.0381 6.62
17 0.0590 0.0325 0.0522 0.0380 6.57
18 0.0513 0.0326 0.0477 0.0381 6.53
19 0.0452 0.0327 0.0443 0.0381 6.50
20 0.0424 0.0329 0.0394 0.0381 6.51
21 0.0426 0.0329 0.0323 0.0381 6.51
22 0.0433 0.0329 0.0248 0.0381 6.51
23 0.0417 0.0328 0.0214 0.0381 6.50
24 0.0373 0.0327 0.0240 0.0382 6.48
25 0.0319 0.0326 0.0277 0.0382 6.45
Elapsed time is 0.003487 seconds.
Reporting
K = length(history.objval);
h = figure;
plot(1:K, history.objval, 'k', 'MarkerSize', 10, 'LineWidth', 2);
ylabel('f(x^k) + g(z^k)'); xlabel('iter (k)');
g = figure;
subplot(2,1,1);
semilogy(1:K, max(1e-8, history.r_norm), 'k', ...
1:K, history.eps_pri, 'k--', 'LineWidth', 2);
ylabel('||r||_2');
subplot(2,1,2);
semilogy(1:K, max(1e-8, history.s_norm), 'k', ...
1:K, history.eps_dual, 'k--', 'LineWidth', 2);
ylabel('||s||_2'); xlabel('iter (k)');
