Exercise 4.3: Solve a simple QP with inequality constraints
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, 4 equality constraints
For improved efficiency, sedumi is solving the dual problem.
------------------------------------------------------------
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 = 4, order n = 9, dim = 12, blocks = 2
nnz(A) = 16 + 0, nnz(ADA) = 16, nnz(L) = 10
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 7.22E+01 0.000
1 : 1.10E+01 1.72E+01 0.000 0.2376 0.9000 0.9000 2.11 1 1 1.1E+00
2 : 9.99E+00 4.77E+00 0.000 0.2778 0.9000 0.9000 1.15 1 1 3.8E-01
3 : 1.04E+01 1.25E+00 0.000 0.2626 0.9000 0.9000 0.96 1 1 1.2E-01
4 : 1.03E+01 2.96E-01 0.000 0.2368 0.9000 0.9000 0.96 1 1 3.2E-02
5 : 1.03E+01 6.69E-02 0.000 0.2256 0.9000 0.9000 0.98 1 1 7.7E-03
6 : 1.03E+01 6.03E-03 0.098 0.0902 0.9900 0.9901 0.99 1 1 7.3E-04
7 : 1.03E+01 1.14E-04 0.000 0.0190 0.9901 0.9900 1.00 1 1 1.5E-05
8 : 1.03E+01 2.96E-08 0.146 0.0003 0.9999 0.9999 1.00 1 1 4.3E-09
iter seconds digits c*x b*y
8 0.1 8.4 1.0317307761e+01 1.0317307722e+01
|Ax-b| = 4.0e-09, [Ay-c]_+ = 1.4E-09, |x|= 3.7e+01, |y|= 3.1e+00
Detailed timing (sec)
Pre IPM Post
0.000E+00 5.000E-02 0.000E+00
Max-norms: ||b||=22, ||c|| = 2,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 2.44525.
------------------------------------------------------------
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