Title: ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions
Authors: Stefan Wild, Rommel Regis, Christine Shoemaker
Abstract: We present a new derivative-free algorithm, ORBIT, for unconstrained local optimization of computationally expensive functions. A trust-region framework using interpolating Radial Basis Function (RBF) models is employed. The RBF models considered often allow ORBIT to interpolate nonlinear functions using fewer function evaluations than the polynomial models considered by present techniques. Approximation guarantees are obtained by ensuring that a subset of the interpolation points are sufficiently poised for linear interpolation. The RBF property of conditional positive definiteness yields a natural method for adding additional points.
We present numerical results on test problems to motivate the use of ORBIT when only a relatively small number of expensive function evaluations are available. Results on two very different application problems, calibration of a watershed model and optimization of a PDE-based bioremediation plan, are also very encouraging and support ORBIT's effectiveness on blackbox functions for which no special mathematical structure is known or available.
Keywords: Derivative-Free Optimization, Radial Basis Functions, Trust-Region Methods, Nonlinear Optimization
Thanks: This work was supported by a Department of Energy Computational Science Graduate Fellowship, grant number DE-FG02-97ER25308 and NSF grants BES-0229176 and CCF-0305583. This research was conducted using the resources of the Cornell Theory Center, which receives funding from Cornell University, New York State, federal agencies, foundations, and corporate partners.
Status: Appears in SIAM Journal on Scientific Computing, Vol. 30 (6), pp. 3197-3219, 2008.
Link: [DOI: 10.1137/070691814]
    author      = "Stefan M. Wild and Rommel G. Regis and Christine A. Shoemaker",
    title       = "{ORBIT:} Optimization by Radial Basis Function Interpolation in Trust-Regions",
    journal     = "SIAM J.~on Scientific Computing",  
    volume      = "30", 
    year        = "2008",
    number      = "6",
    pages       = "3197--3219",
    doi         = "10.1137/070691814"
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