Cao Liyuan, Postdoctor, Beijing International Center for Mathematical Research, Peking University

Li Zhang, Doctor

The Error of Multivariate Linear Extrapolation with Applications to Derivative-Free Optimization

16:00-17:00 July 1(Monday), Z311

Comparing to linear interpolation in its narrow sense, linear extrapolation is used more often in derivative-free optimization, but its error is not well-studied. We present a numerical method to compute the sharp bound on the error, as well as several analytical bounds along with the conditions under which they are sharp. Additionally, we provide the convergence theories regarding a simplex derivative-free optimization method to demonstrate the utility of the derived bounds. All results are under the assumptions that the function being interpolated has Lipschitz continuous gradient and is interpolated on an affinely independent sample set.

个人简介：Liyuan Cao is a postdoctoral researcher at BICMR, Peking University under the supervision of Prof. Zaiwen Wen. He received his PhD from the Industrial and Systems Engineering Department at Lehigh University in 2021 under Prof. Katya Scheinberg. His research focuses on the analysis and development of algorithms in nonlinear optimization and derivative-free optimization.