Exercise 4.38(b): Linear matrix inequalities with one variable
randn('state',0);
n = 4;
A = randn(n); A = 0.5*(A'+A);
B = randn(n); B = B'*B;
c = -1;
cvx_begin sdp
variable t
minimize ( c*t )
A >= t * B;
cvx_end
disp('------------------------------------------------------------------------');
disp('The optimal t obtained is');
disp(t);
Calling sedumi: 10 variables, 1 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 = 1, order n = 5, dim = 17, blocks = 2
nnz(A) = 10 + 0, nnz(ADA) = 1, nnz(L) = 1
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 8.07E+00 0.000
1 : -6.80E-01 1.51E+00 0.000 0.1867 0.9000 0.9000 0.45 1 1 1.9E+00
2 : -2.18E+00 3.25E-01 0.000 0.2156 0.9000 0.9000 0.04 1 1 1.1E+00
3 : -1.52E+01 2.54E-02 0.000 0.0781 0.9900 0.9900 -0.60 1 1 5.7E-01
4 : -4.19E+01 2.24E-03 0.000 0.0881 0.9900 0.9900 -0.27 1 1 1.2E-01
5 : -4.72E+01 3.75E-04 0.000 0.1678 0.9000 0.9000 0.96 1 1 2.0E-02
6 : -4.83E+01 8.86E-07 0.149 0.0024 0.9955 0.9990 0.99 1 1 1.5E-04
7 : -4.83E+01 1.70E-07 0.000 0.1923 0.9000 0.6868 1.00 1 1 2.9E-05
8 : -4.83E+01 4.71E-09 0.058 0.0277 0.9903 0.9900 1.00 1 1 6.7E-07
9 : -4.83E+01 6.95E-10 0.000 0.1475 0.9000 0.8343 1.00 1 1 1.3E-07
10 : -4.83E+01 3.33E-11 0.360 0.0479 0.9905 0.9900 1.00 1 1 5.6E-09
iter seconds digits c*x b*y
10 0.1 Inf -4.8318982940e+01 -4.8318982370e+01
|Ax-b| = 6.4e-10, [Ay-c]_+ = 8.5E-09, |x|= 1.1e+02, |y|= 2.6e+02
Detailed timing (sec)
Pre IPM Post
2.000E-02 1.000E-01 0.000E+00
Max-norms: ||b||=1.877157e-01, ||c|| = 2.895108e+00,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.
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Status: Solved
Optimal value (cvx_optval): +48.354
------------------------------------------------------------------------
The optimal t obtained is
-48.3540