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

TitleGlobal Convergence of Radial Basis Function Trust-Region Algorithms for Derivative-Free Optimization
Publication TypeJournal Article
Year of Publication2013
AuthorsWild, SM, Shoemaker, C
JournalSIAM Review
Volume55
Issue2
Pagination349-371
Other NumbersANL/MCS-P3097-1212
AbstractWe 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 [SIAM J. Optim., 20 (2009), pp. 387–415] 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 [SIAM J. Sci. Comput., 30 (2008), pp. 3197–3219]. 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 involving remediation of contaminated groundwater.  
DOI10.1137/120902434
PDFhttp://www.mcs.anl.gov/papers/P3097-1212_1.pdf