Xin Tong : A Locally Adaptive Algorithm for Global Minimization of Univariate Functions

Posted by David Reynolds , part of the Graduate Analysis Seminar.

At

May 2, 2018, 4 p.m.

In

SEO 512

Abstract

In this talk, I will introduce a locally adaptive algorithm for global minimization of univariate functions on a bounded interval. These functions are smooth and not too highly oscillatory, but are not necessarily convex, in the Sobolev space $W_2^{\infty}$. This algorithm samples more function values where the function is small in value and more spiky. It provides an estimated minimum that satisfies a user-specified absolute error tolerance. This algorithm, called funmin_g, is implemented in the Guaranteed Automatic Integrate Library (GAIL). There are numerical examples that illustrate its superior performance in comparison to other more established solvers including MATLAB's fminbnd and Chebfun's min.