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.