n = 2;
randn('state',3);
N = 10; M = 6;
Y = [1.5+1*randn(1,M); 2*randn(1,M)];
X = [-1.5+1*randn(1,N); 2*randn(1,N)];
T = [-1 1; 1 1];
Y = T*Y; X = T*X;
cvx_begin
variables a(n) b(1) t(1)
maximize (t)
X'*a - b >= t;
Y'*a - b <= -t;
norm(a) <= 1;
cvx_end
linewidth = 0.5;
t_min = min([X(1,:),Y(1,:)]);
t_max = max([X(1,:),Y(1,:)]);
tt = linspace(t_min-1,t_max+1,100);
p = -a(1)*tt/a(2) + b/a(2);
p1 = -a(1)*tt/a(2) + (b+t)/a(2);
p2 = -a(1)*tt/a(2) + (b-t)/a(2);
graph = plot(X(1,:),X(2,:), 'o', Y(1,:), Y(2,:), 'o');
set(graph(1),'LineWidth',linewidth);
set(graph(2),'LineWidth',linewidth);
set(graph(2),'MarkerFaceColor',[0 0.5 0]);
hold on;
plot(tt,p, '-r', tt,p1, '--r', tt,p2, '--r');
axis equal
title('Robust linear discrimination problem');
Calling sedumi: 20 variables, 5 equality constraints
For improved efficiency, sedumi is solving the dual problem.
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SeDuMi 1.21 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 5, order n = 20, dim = 21, blocks = 2
nnz(A) = 68 + 0, nnz(ADA) = 21, nnz(L) = 13
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 4.69E+01 0.000
1 : -3.49E-01 1.71E+01 0.000 0.3637 0.9000 0.9000 2.59 1 1 9.9E+00
2 : 7.65E-03 5.42E+00 0.000 0.3177 0.9000 0.9000 2.36 1 1 2.4E+00
3 : 2.62E-01 1.27E+00 0.000 0.2336 0.9000 0.9000 0.23 1 1 1.0E+00
4 : 4.73E-01 3.00E-01 0.000 0.2372 0.9000 0.9000 0.58 1 1 2.7E-01
5 : 5.05E-01 2.91E-02 0.000 0.0969 0.9900 0.9900 0.98 1 1 2.7E-02
6 : 5.11E-01 1.39E-05 0.000 0.0005 0.9999 0.9999 1.00 1 1 1.5E-05
7 : 5.11E-01 1.04E-06 0.290 0.0748 0.9900 0.9900 1.00 1 1 1.1E-06
8 : 5.11E-01 1.96E-07 0.000 0.1874 0.9000 0.9063 1.00 1 1 2.2E-07
9 : 5.11E-01 2.87E-09 0.000 0.0147 0.9901 0.9900 1.00 1 1 3.3E-09
iter seconds digits c*x b*y
9 0.0 8.6 5.1122989899e-01 5.1122989774e-01
|Ax-b| = 1.6e-09, [Ay-c]_+ = 3.3E-11, |x|= 1.1e+00, |y|= 1.2e+00
Detailed timing (sec)
Pre IPM Post
0.000E+00 5.000E-02 0.000E+00
Max-norms: ||b||=1, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.51123