The MOSEK Python optimizer API manual Version 7.0 (Revision 141)

242 APPENDIX A. API REFERENCE
Description:
Let (s x n) ∗ be the value of variable (s x n) for the specified solution. For simplicity let us assume
that s x n is a member of quadratic cone, then the violation is computed as follows
{
max(0, ‖(s
x
n ) 2;n ‖ ∗ − (s x n) ∗ 1)/ √ 2, (s x n) ∗ ≥ − ‖(s x n) ∗ 2:n‖ ,
‖(s x n) ∗ ‖ ,
otherwise.
Both when the solution is a certificate of primal infeasibility or when it is a dual feasibible
solution the violation should be small.
A.2.70
Task.getdviolvar()
Task.getdviolvar(
whichsol,
sub,
viol)
Computes the violation of a dual solution associated with a set of x variables.
Arguments
sub : int[]
An array of indexes of x variables.
viol : double[]
viol[k] is the maximal violation of the solution for the constraints (s x l ) sub[k]
(s x u) sub[k] ≥ 0.
whichsol : soltype
Selects a solution.
≥ 0 and
Description:
The violation fo dual solution associated with the j’th variable is computed as follows
where
max(ρ((s x l ) ∗ i , (b x l ) i ), ρ((s x u) ∗ i , −(b x u) i ), | ∑ j = 0 numcon−1 a ij y i + (s x l ) ∗ i − (s x u) ∗ i − τc j |)
{ − x, l > −∞,
ρ(x, l) =
|x|, otherwise
τ = 0 if the the solution is certificate of dual infeasibility and τ = 1 otherwise. The formula for
computing the violation is only shown for linear case but is generalized approriately for the more
general problems.