Figure 8.9: Robust linear discrimination problem
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: 19 variables, 4 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 = 4, order n = 19, dim = 20, blocks = 2
nnz(A) = 66 + 0, nnz(ADA) = 16, nnz(L) = 10
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 4.94E+01 0.000
1 : -4.50E-01 1.38E+01 0.000 0.2788 0.9000 0.9000 2.41 1 1 8.3E+00
2 : -8.82E-03 4.04E+00 0.000 0.2933 0.9000 0.9000 1.89 1 1 2.3E+00
3 : 2.12E-01 1.48E+00 0.000 0.3658 0.9000 0.9000 -0.01 1 1 1.4E+00
4 : 4.41E-01 5.14E-01 0.000 0.3479 0.9000 0.9000 0.79 1 1 4.6E-01
5 : 5.04E-01 4.10E-02 0.000 0.0799 0.9900 0.9900 0.89 1 1 3.8E-02
6 : 5.11E-01 2.03E-04 0.000 0.0049 0.9990 0.9990 0.99 1 1 1.9E-04
7 : 5.11E-01 4.04E-08 0.000 0.0002 0.9999 0.9999 1.00 1 1 4.0E-08
8 : 5.11E-01 1.01E-08 0.000 0.2494 0.9035 0.9000 1.00 1 1 1.0E-08
iter seconds digits c*x b*y
8 0.0 8.3 5.1122990003e-01 5.1122989767e-01
|Ax-b| = 7.9e-09, [Ay-c]_+ = 1.9E-10, |x|= 9.5e-01, |y|= 1.2e+00
Detailed timing (sec)
Pre IPM Post
0.000E+00 4.000E-02 0.000E+00
Max-norms: ||b||=1, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.75957.
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Status: Solved
Optimal value (cvx_optval): +0.51123