||Global Convergence of Radial Basis Function Trust Region Derivative-Free Algorithms
||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.
||Derivative-Free Optimization, Radial Basis Functions, Trust Region Methods, Nonlinear Optimization
||Wild's work supported by a DOE Computational Science Graduate Fellowship under grant number DE-FG02-97ER25308, by an Argonne Director's Postdoctoral Fellowship, and by DOE under contract DE-AC02-06CH11357. Shoemaker's work supported by NSF grants BES-022917, CBET-0756575, CCF-0305583, and DMS-0434390.
||Appears in SIAM J. Optimization, Vol. 21 (3), pp.761-781, 2011.
|| [DOI: 10.1137/09074927X]
||Titled Global Convergence of Radial Basis Function Trust-Region Algorithms,
Argonne Preprint ANL/MCS-P1580-0209.|
author = "Stefan M. Wild and Christine A. Shoemaker",
title = "Global Convergence of Radial Basis Function Trust Region Derivative-Free Algorithms",
journal = "SIAM J.~Optimization",
volume = "21",
year = "2011",
number = "3",
pages = "761--781",
doi = "10.1137/09074927X"