XSLP_XTOL_A, SLPXTOL_A

It may happen that all the variables have converged, but some have converged on extended criteria and at least one of these variables is at its step bound. This means that, at least in the linearization, if the variable were to be allowed to move further the objective function would improve. This does not necessarily imply that the same is true of the original problem, but it is still possible that an improved result could be obtained by taking another SLP iteration. However, if the objective function has already been stable for several SLP iterations, then there is less likelihood of an improved result, and the converged solution can be accepted.

The static objective function (1) test measures the significance of the changes in the objective function over recent SLP iterations. It is applied when all the variables have converged, but some have converged on extended criteria and at least one of these variables is at its step bound. Because all the variables have converged, the solution is already converged but the fact that some variables are at their step bound limit suggests that the objective function could be improved by going further.

The variation in the objective function is defined as
δObj = MAX_Iter(Obj) - MIN_Iter(Obj)
where Iter is the XSLP_XCOUNT most recent SLP iterations and Obj is the corresponding objective function value.

If ABS(δObj) ≤ XSLP_XTOL_A
then the objective function is deemed to be static according to the absolute static objective function (1) criterion.
If ABS(δObj) ≤ AVG_Iter(Obj) * XSLP_XTOL_R
then the objective function is deemed to be static according to the relative static objective function (1) criterion.

The static objective function (1) test is applied only until XSLP_XLIMIT SLP iterations have taken place. After that, if all the variables have converged on strict or extended criteria, the solution is deemed to have converged.

If the objective function passes the relative or absolute static objective function (1) test then the solution is deemed to have converged.

When the value is set to be negative, the value is adjusted automatically by SLP, based on the optimality target XSLP_VALIDATIONTARGET_K. Good values for the control are usually fall between 1e-3 and 1e-6.