Title: Global Convergence of Radial Basis Function Trust Region Derivative-Free Algorithms
Authors: Stefan Wild, Christine Shoemaker
Abstract: 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.
Keywords: Derivative-Free Optimization, Radial Basis Functions, Trust Region Methods, Nonlinear Optimization
Thanks: 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.
Status: Appears in SIAM J. Optimization, Vol. 21 (3), pp.761-781, 2011.
Link: [DOI: 10.1137/09074927X]
Formerly: 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"
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