crosses the centre line of a cell, causing a discontinuous change in the actual object size, and hence in the simulation results. On small scales, therefore, the partial derivatives of any penalty function will be zero in most places, with delta-functions sprinkled round, and the penalty function surfaces exhibit multidimensional cliffs and canyons. This is why we’re not using one of those fancy variable metric optimizers. POEMS has no way of exploring the bottom of a canyon it never encounters, so for simulations with significant economic importance, it’s worth restarting the simulator a few times using the RESTARTS parameter of the COMPUTE statement. (For more discussion, see e.g. W. H. Press et al, Numerical Recipes in C, 2nd Ed., Cambridge (UK), Cambridge University Press, 1991.
