CECM Colloquium

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.