Berkeley Lab Scientific Computing Seminar

For instance, at each iteration of a pattern search method, one can attempt to compute an accurate simplex gradient by identifying a sampling set of previous iterates with good geometrical properties. This simplex gradient can then be used to reorder the evaluations of the objective function associated with the positive spanning set or positive basis used in the poll step. But it can also be used to update the mesh size parameter according to a sufficient decrease criterion. None of these modifications demands new function evaluations. Surrogate-models based on simplex derivatives can also be considered in the search step.

We will present these procedures in detail and apply them to a set of problems which includes test problems from the CUTEr collection and two applications problems (one related to the simulation of a mechanical system with contact and another resulting from parameter estimation in astrophysics). The numerical results show that these procedures can enhance significantly the practical performance of pattern search methods.