Title: Mesh Adaptive Direct Search Algorithms

This talk introduces the Mesh Adaptive Direct Search (MADS) class of algorithms for nonlinear optimization. MADS is a derivative-free class of simple algorithms intended to overcome the directional dependencies of the earlier GPS algorithms. Our intention is to have MADS replace GPS in software presently in use by our industrial collaborators. MADS is applicable to a wider class of problems than GPS, including yes/no constraints, and in preliminary tests, MADS seems more efficient.
MADS came about because our nonsmooth analysis of GPS made clear deficiencies glossed over by assuming smoothness. Thus, our aim was that MADS have a more satisfying convergence theory based on the Clarke calculus and Rockafeller's notion of a hypertangent cone.
This research was done in collaboration with: CoPI Charles Audet and Gilles Couture, Ecole Polytechnique de Montreal, and Lt Col Mark Abramson, AFIT.