Global Convergence of Radial Basis Function Trust Region Derivative-Free Algorithms

TitleGlobal Convergence of Radial Basis Function Trust Region Derivative-Free Algorithms
Publication TypeJournal Article
Year of Publication2009
AuthorsWild, SM, Shoemaker, C
Date Published02/2009
Other NumbersANL/MCS-P1580-0209
Abstract

<p>We analyze globally convergent derivative-free trust region algorithms relying on radial basis function interpolation models. Our results extend the recent work of Conn, Scheinberg, and Vicente to fully linear models that have a nonlinear term. We characterize the types of radial basis functions that fit in our analysis and thus show global convergence to first-order critical points for the ORBIT algorithm of Wild, Regis and Shoemaker. Using ORBIT, we present numerical results for different types of radial basis functions on a series of test problems. We also demonstrate the use of ORBIT in finding local minima on a computationally expensive environmental engineering problem.</p>

PDFhttp://www.mcs.anl.gov/papers/P1580.pdf