b = [2; 0.2; -0.3];
n = length( b );
cvx_begin sdp
variable X( n, n ) symmetric
dual variable y{n}
minimize( ( n - 1 : -1 : 0 ) * diag( X ) );
for k = 1 : n,
sum( diag( X, k - 1 ) ) == b( k ) : y{k};
end
X >= 0;
cvx_end
y = [ y{:} ]';
disp( 'The optimal point, X:' );
disp( X )
disp( 'The diagonal sums:' );
disp( sum( spdiags( X, 0:n-1 ), 1 ) );
disp( 'min( eig( X ) ) (should be nonnegative):' );
disp( min( eig( X ) ) )
disp( 'The optimal weighted trace:' );
disp( ( n - 1 : -1 : 0 ) * diag( X ) );
Calling sedumi: 6 variables, 3 equality constraints
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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 = 3, order n = 4, dim = 10, blocks = 2
nnz(A) = 6 + 0, nnz(ADA) = 9, nnz(L) = 6
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 1.78E+00 0.000
1 : -3.54E+00 4.11E-01 0.000 0.2312 0.9000 0.9000 1.39 1 1 1.4E+00
2 : -3.76E+00 3.39E-02 0.000 0.0824 0.9900 0.9900 1.31 1 1 1.0E-01
3 : -3.88E+00 1.18E-05 0.000 0.0003 0.9999 0.9999 0.99 1 1 3.6E-05
4 : -3.88E+00 5.45E-07 0.000 0.0463 0.9900 0.9900 1.00 1 1 1.7E-06
5 : -3.88E+00 2.48E-08 0.000 0.0455 0.9900 0.9900 1.00 1 1 7.6E-08
6 : -3.88E+00 2.01E-09 0.329 0.0812 0.9900 0.9900 0.99 2 2 6.2E-09
iter seconds digits c*x b*y
6 0.0 Inf -3.8772674402e+00 -3.8772674352e+00
|Ax-b| = 5.4e-09, [Ay-c]_+ = 2.9E-09, |x|= 2.0e+00, |y|= 2.2e+00
Detailed timing (sec)
Pre IPM Post
0.000E+00 3.000E-02 0.000E+00
Max-norms: ||b||=2, ||c|| = 2,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.122733
The optimal point, X:
0.0468 -0.0369 -0.3000
-0.0369 0.0292 0.2369
-0.3000 0.2369 1.9240
The diagonal sums:
2.0000 0.2000 -0.3000
min( eig( X ) ) (should be nonnegative):
-4.7117e-09
The optimal weighted trace:
0.1227