XSLP_ITOL

The relative impact convergence criterion assesses the change in the effect of a coefficient in a constraint in relation to the magnitude of the constituents of the constraint. The effect of a coefficient is its value multiplied by the activity of the column in which it appears.

E = X * C

where X is the activity of the matrix column in which the coefficient appears, and C is the value of the coefficient. The linearization approximates the effect of the coefficient as

E₁ = X * C₀ + X * C'₀

where X is as before, C₀ is the value of the coefficient C calculated using the assumed values for the variables and C'₀ is the value of

C

X

calculated using the assumed values for the variables.
If C₁ is the value of the coefficient C calculated using the actual values for the variables, then the error in the effect of the coefficient is given by

E = X * C₁ - (X * C₀ + X * C'₀)

All the elements of the constraint are examined, excluding delta and error vectors: for each, the contribution to the constraint is evaluated as the element multiplied by the activity of the vector in which it appears; it is then included in a total positive contribution or total negative contribution depending on the sign of the contribution. If the predicted effect of the coefficient is positive, it is tested against the total positive contribution; if the effect of the coefficient is negative, it is tested against the total negative contribution. If T₀ is the total positive or total negative contribution to the constraint (as appropriate)
and E < T₀*XSLP_ITOL_R
then the variable has passed the relative impact convergence criterion for this coefficient.
If a variable which has not converged on strict (closure or delta) criteria passes the (relative or absolute) impact or matrix criteria for all the coefficients in which it appears, then it is deemed to have converged.