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

Stefan Wild (wild***at***mcs.anl.gov)
Christine Shoemaker (cas12***at***cornell.edu)

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.

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Nonlinear Optimization (Other )

Category 3: Applications -- Science and Engineering (Civil and Environmental Engineering )

Citation: Appears in SIAM Journal on Optimization, Vol. 21 (3), pp.761-781, 2011. Formerly: Argonne Preprint ANL/MCS-P1580-0209.

Download: [PDF]

Entry Submitted: 04/29/2011
Entry Accepted: 04/29/2011
Entry Last Modified: 09/19/2011

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