Over the course of my career, continuous nonlinear optimization has come into its own as a crucial area of computational and applied mathematics. When I got my degree in 1966, it was generally true that the available algorithms could not solve the problems encountered by an industrial design engineer. I do not think this is true any longer. A large part of this advancement has been the resurgence of interest in derivative-free algorithms.
I will introduce you to, or remind you of, the class of problems we can now solve using derivative-free methods. These problems are small, very expensive, and they have some universal properties not usually mentioned in polite conversation in the halls of academe. I will not talk about our approaches to these problems, but I will give some practical successes of our algorithms as evidence of the importance of this class of problems, and I will outline two extensions needed now for this class of problems by industrial designers. Specifically, I will mention nonlinear robust optimization and optimization with conflicting objectives. Although I have worked on the really hard and important areas of multidisciplinary design optimization and distributed optimization, these are beyond the scope of a single talk.
JEDennisPoster-biography.pdf (250 Ko)