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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, 2
nd
Ed., Cambridge (UK), Cambridge University Press, 1991.
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