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: 11 variables (1 free), 10 equality constraints
------------------------------------------------------------------------
SeDuMi 1.1 by AdvOL, 2005 and Jos F. Sturm, 1998, 2001-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
Split 1 free variables
eqs m = 10, order n = 7, dim = 19, blocks = 2
nnz(A) = 30 + 0, nnz(ADA) = 100, nnz(L) = 55
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 3.07E+000 0.000
1 : 2.85E+000 5.77E-001 0.000 0.1879 0.9000 0.9000 -0.13 1 1 1.8E+000
2 : 1.04E+001 1.11E-001 0.000 0.1923 0.9000 0.9000 -0.24 1 1 1.2E+000
3 : 7.35E+001 6.93E-003 0.000 0.0625 0.9900 0.9900 -0.68 1 1 5.5E-001
4 : 6.79E+001 6.76E-004 0.000 0.0974 0.9900 0.9900 0.03 1 1 8.8E-002
5 : 4.84E+001 6.55E-006 0.000 0.0097 0.9990 0.9990 1.02 1 1 8.3E-004
6 : 4.84E+001 4.86E-007 0.000 0.0742 0.9000 0.7177 1.00 1 1 2.3E-004
7 : 4.84E+001 9.20E-008 0.000 0.1892 0.9000 0.9032 1.00 1 2 4.1E-005
8 : 4.84E+001 3.01E-009 0.000 0.0328 0.9813 0.9900 1.00 2 2 1.8E-006
9 : 4.84E+001 6.70E-010 0.000 0.2224 0.9000 0.9000 1.00 2 2 4.1E-007
10 : 4.84E+001 3.58E-011 0.000 0.0534 0.9900 0.9900 1.00 2 3 2.2E-008
11 : 4.84E+001 3.38E-012 0.438 0.0945 0.9900 0.9900 1.00 3 3 2.1E-009
iter seconds digits c*x b*y
11 0.1 Inf 4.8354031400e+001 4.8354031573e+001
|Ax-b| = 7.6e-010, [Ay-c]_+ = 1.0E-009, |x|= 5.4e+002, |y|= 1.4e+002
Detailed timing (sec)
Pre IPM Post
0.000E+000 5.007E-002 0.000E+000
Max-norms: ||b||=1.406028e+000, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 177.293.
------------------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +48.354
------------------------------------------------------------------------
The optimal t obtained is
-48.3540