XSLP_WTOL_R

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.

The extended convergence continuation criterion is applied after a converged solution has been found where at least one variable has converged on extended criteria and is at its step bound limit. The extended convergence continuation test measures whether any improvement is being achieved when additional SLP iterations are carried out. If not, then the last converged solution will be restored and the optimization will stop.
For a maximization problem, the improvement in the objective function at the current iteration compared to the objective function at the last converged solution is given by:
δObj = Obj - LastConvergedObj
For a minimization problem, the sign is reversed.
If δObj > XSLP_WTOL_A and
δObj > ABS(ConvergedObj) * XSLP_WTOL_R then the solution is deemed to have a significantly better objective function value than the converged solution.

If XSLP_WCOUNT is greater than zero, and a solution is found which converges on extended criteria and with active step bounds, the solution is saved and SLP optimization continues until one of the following:
(1) a new solution is found which converges on some other criterion, in which case the SLP optimization stops with this new solution;
(2) a new solution is found which converges on extended criteria and with active step bounds, and which has a significantly better objective function, in which case this is taken as the new saved solution;
(3) none of the XSLP_WCOUNT most recent SLP iterations has a significantly better objective function than the saved solution, in which case the saved solution is restored and the SLP optimization stops.

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-4 and 1e-6.