Journal
SIAM REVIEW
Volume 55, Issue 2, Pages 349-371Publisher
SIAM PUBLICATIONS
DOI: 10.1137/120902434
Keywords
derivative-free optimization; radial basis functions; trust-region methods; nonlinear optimization
Categories
Funding
- Argonne, a U.S. Department of Energy (DOE) Office of Science laboratory [DE-AC02-06CH11357]
- DOE Computational Science Graduate Fellowship [DE-FG02-97ER25308]
- Applied Mathematics activity within the DOE Office of Science's Advanced Scientific Computing Research program
- NSF [BES-022917, CBET-0756575, CCF-0305583, DMS-0434390]
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1116298] Funding Source: National Science Foundation
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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 [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.
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