We are given the primal-dual pair of problems
st. x in K
Ax = b
st. z in K
A^T y + z = c
i) the violation of the affine constraints normalized:
norm(Ax - b)/(1+max(abs(b))), norm(A^T y + z - c)(1+max(abs(c)))
ii) the violation of the conic constraints:
For this purpose, we suggest computing min(eigK(x)) and min(eigK(z)) by using Sedumi's eigK function.
iii) Some codes do not explicitly maintain z. In this case,
one should set
s = c - A^T yOf course, then the violation as in i) will be zero (depending on the accuracy achieved by the computer).
Finally, the duality gap:
max(0, c'*x - b'*y)
To make all error computations consistent, please use the