P = [0.70 0.10
0.20 0.10
0.05 0.70
0.05 0.10];
[n,m] = size(P);
nopts = 1000;
weights = logspace(-5,5,nopts);
obj = [0;1];
inds = ones(n,1);
next = 2;
for i = 1 : nopts,
PW = P * diag( [ 1 ; weights(i) ] );
[ maxvals, maxinds ] = max( PW' );
if (~isequal(maxinds', inds(:,next-1)))
inds(:,next) = maxinds';
T = zeros(m,n);
for j=1:n
T(maxinds(1,j),j) = 1;
end;
obj(:,next) = 1-diag(T*P);
next = next+1;
end;
end;
plot(obj(1,:), obj(2,:),[0 1], [0 1],'--');
grid on
for i=2:size(obj,2)-1
text(obj(1,i),obj(2,i),['a', num2str(i-1)]);
end;
cvx_begin
variables T( m, n ) D( m, m )
minimize max( D(1,2), D(2,1) )
subject to
D == T * P;
sum( T, 1 ) == 1;
T >= 0;
cvx_end
objmp = 1 - diag( D );
text( objmp(1), objmp(2), 'b' );
xlabel('P_{fp}'); ylabel('P_{fn}');
Calling sedumi: 10 variables, 5 equality constraints
------------------------------------------------------------
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 = 11, dim = 11, blocks = 1
nnz(A) = 18 + 0, nnz(ADA) = 13, nnz(L) = 9
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 3.84E+00 0.000
1 : 4.94E-01 1.11E+00 0.000 0.2891 0.9000 0.9000 3.24 1 1 7.1E-01
2 : 2.26E-01 2.18E-01 0.000 0.1960 0.9000 0.9000 1.25 1 1 1.7E-01
3 : 1.82E-01 5.12E-02 0.000 0.2353 0.9000 0.9000 1.05 1 1 4.6E-02
4 : 1.68E-01 4.07E-03 0.000 0.0794 0.9900 0.9900 1.01 1 1 4.0E-03
5 : 1.67E-01 1.65E-06 0.000 0.0004 0.9999 0.9999 1.00 1 1
iter seconds digits c*x b*y
5 0.0 Inf 1.6666666667e-01 1.6666666667e-01
|Ax-b| = 1.6e-16, [Ay-c]_+ = 0.0E+00, |x|= 1.9e+00, |y|= 3.5e-01
Detailed timing (sec)
Pre IPM Post
0.000E+00 2.000E-02 0.000E+00
Max-norms: ||b||=1, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.166667