Answer by Arne Stolbjerg Drud:
The SLP solver inside CONOPT is used to find good search directions by approximately solving a linear approximation to the model in the current point. However, CONOPT uses a linesearch in this direction and uses the final basis from the LP to restore feasibility. This is different from 'classical SLP'. In CONOPT we start from a feasible point and feasibility is restored outside the SLP framework. In classical SLP feasibility and change in objective are handled simultaneously by the SLP.
Or to answer your question: you cannot use the SLP algorithm exclusively - you cannot even control when it is used. This is based on observations of the behavior of your model in previous iterations.