P = [13 12 -2; 12 17 6; -2 6 12];
q = [-22; -14.5; 13];
r = 1;
n = 3;
x_star = [1;1/2;-1];
fprintf(1,'Computing the optimal solution ...');
cvx_begin
variable x(n)
minimize ( (1/2)*quad_form(x,P) + q'*x + r)
x >= -1;
x <= 1;
cvx_end
fprintf(1,'Done! \n');
disp('------------------------------------------------------------------------');
disp('The computed optimal solution is: ');
disp(x);
disp('The given optimal solution is: ');
disp(x_star);
Computing the optimal solution ...
Calling sedumi: 11 variables, 7 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 = 7, order n = 9, dim = 12, blocks = 2
nnz(A) = 17 + 0, nnz(ADA) = 33, nnz(L) = 20
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 2.75E+00 0.000
1 : -3.71E+01 7.86E-01 0.000 0.2860 0.9000 0.9000 2.64 1 1 8.3E-01
2 : -5.38E+01 1.87E-01 0.000 0.2381 0.9000 0.9000 1.14 1 1 1.9E-01
3 : -5.78E+01 4.88E-02 0.000 0.2607 0.9000 0.9000 0.95 1 1 5.2E-02
4 : -5.88E+01 1.20E-02 0.000 0.2464 0.9000 0.9000 0.95 1 1 1.3E-02
5 : -5.90E+01 2.77E-03 0.000 0.2306 0.9000 0.9000 0.97 1 1 3.0E-03
6 : -5.91E+01 4.56E-04 0.000 0.1647 0.9015 0.9000 0.99 1 1 5.7E-04
7 : -5.91E+01 4.96E-06 0.000 0.0109 0.9901 0.9900 1.00 1 1 1.3E-05
8 : -5.91E+01 2.30E-10 0.000 0.0000 0.9999 0.9969 1.00 1 1 2.8E-08
9 : -5.91E+01 1.37E-11 0.000 0.0596 0.9450 0.9475 1.00 2 2 1.6E-09
iter seconds digits c*x b*y
9 0.1 Inf -5.9124999997e+01 -5.9124999919e+01
|Ax-b| = 5.9e-10, [Ay-c]_+ = 1.8E-08, |x|= 4.2e+00, |y|= 3.0e+01
Detailed timing (sec)
Pre IPM Post
1.000E-02 5.000E-02 1.000E-02
Max-norms: ||b||=2, ||c|| = 4.268278e+01,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.631.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -21.625
Done!
------------------------------------------------------------------------
The computed optimal solution is:
1.0000
0.5000
-1.0000
The given optimal solution is:
1.0000
0.5000
-1.0000