XSLP_MTOL

The relative effective matrix element convergence criterion assesses the change in the effect of a coefficient in a constraint relative to the magnitude of the coefficient. 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 V 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)

If E < E₁ * XSLP_MTOL_R
then the variable has passed the relative effective matrix element 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.