p = 1;
n = 10; m = 2*n; q=0.5*n;
A = randn(m,n);
b = randn(m,1);
C = randn(q,n);
d = randn(q,1);
cvx_begin
variable x(n)
dual variable y
minimize( norm( A * x - b, p ) )
subject to
y : C * x == d;
cvx_end
disp( sprintf( 'norm(A*x-b,%g):', p ) );
disp( [ ' ans = ', sprintf( '%7.4f', norm(A*x-b,p) ) ] );
disp( 'Optimal vector:' );
disp( [ ' x = [ ', sprintf( '%7.4f ', x ), ']' ] );
disp( 'Residual vector:' );
disp( [ ' A*x-b = [ ', sprintf( '%7.4f ', A*x-b ), ']' ] );
disp( 'Equality constraints:' );
disp( [ ' C*x = [ ', sprintf( '%7.4f ', C*x ), ']' ] );
disp( [ ' d = [ ', sprintf( '%7.4f ', d ), ']' ] );
disp( 'Lagrange multiplier for C*x==d:' );
disp( [ ' y = [ ', sprintf( '%7.4f ', y ), ']' ] );
Calling sedumi: 50 variables, 25 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
Split 10 free variables
eqs m = 25, order n = 61, dim = 61, blocks = 1
nnz(A) = 540 + 0, nnz(ADA) = 625, nnz(L) = 325
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 4.79E+01 0.000
1 : 1.39E+01 1.66E+01 0.000 0.3464 0.9000 0.9000 2.26 1 1 1.4E+00
2 : 1.89E+01 3.34E+00 0.000 0.2008 0.9000 0.9000 1.25 1 1 3.2E-01
3 : 2.03E+01 6.88E-01 0.000 0.2062 0.9000 0.9000 1.03 1 1 6.9E-02
4 : 2.06E+01 1.58E-01 0.000 0.2292 0.9000 0.9000 1.01 1 1 1.6E-02
5 : 2.06E+01 3.08E-02 0.000 0.1951 0.9000 0.9000 1.00 1 1 3.2E-03
6 : 2.07E+01 1.23E-04 0.000 0.0040 0.9990 0.9989 1.00 1 1
iter seconds digits c*x b*y
6 0.0 15.3 2.0661712233e+01 2.0661712233e+01
|Ax-b| = 7.5e-15, [Ay-c]_+ = 2.0E-15, |x|= 1.1e+01, |y|= 7.5e+00
Detailed timing (sec)
Pre IPM Post
0.000E+00 3.000E-02 0.000E+00
Max-norms: ||b||=2.153708e+00, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.97849.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +20.6617
norm(A*x-b,1):
ans = 20.6617
Optimal vector:
x = [ 0.1655 0.6782 -0.4228 0.9150 -0.0906 0.1216 -0.3164 0.1219 -0.6398 -0.6228 ]
Residual vector:
A*x-b = [ 0.4010 1.7552 1.9558 0.9247 -1.1188 -0.0000 1.5849 -3.1664 1.1300 -2.3871 -0.9826 -0.5744 -0.5122 1.5118 -2.0815 -0.5752 0.0000 -0.0000 -0.0000 0.0000 ]
Equality constraints:
C*x = [ -0.5847 -2.1537 1.3786 0.0757 1.2487 ]
d = [ -0.5847 -2.1537 1.3786 0.0757 1.2487 ]
Lagrange multiplier for C*x==d:
y = [ -1.5438 -5.6554 1.4361 0.3269 -1.8537 ]