Wednesday November 20, 2002 in the K9509, SFU
Dr. Luis N. Vicente,
Department of Mathematics, University of Coimbra, Portugal
IBM T.J. Watson Research Center, Yorktown Heights, New York
Title:"Error Estimates And Poisedness In Multivariate Polynomial Optimization And Derivative-Free Optimization."
Abstract:The purpose of this talk is twofold. We show first how to derive error estimates between a function and its interpolating polynomial and between their corresponding derivatives. The derivation is based on a new concept of well-poisedness for the interpolation set, directly connecting the accuracy of the error estimates with the geometry (well-poisedness) of the points in the set. The prior existing error estimates make use of less intuitive geometrical conditions. Our approach provides also an appropriate algorithmic framework to ensure well-poisedness.
In the other part of the talk, we will briefly describe derivative-free optimization techniques based on geometrical concepts like well-poisedness and positive bases, pointing out what are the key ingredients for convergence and making a link to the first part of the talk.