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

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 characteri...

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Bibliographic Details
Published inSIAM review Vol. 55; no. 2; pp. 349 - 371
Main Authors Wild, Stefan M., Shoemaker, Christine
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Subjects
Algorithms
Applied mathematics
Computer science
Convergence
Engineering
Environmental engineering
Groundwater
Interpolation
Laboratories
Mathematical functions
Mathematical models
Numerical analysis
Optimization
Optimization algorithms
Orbits
Radial basis function
Series (mathematics)
SIGEST
Studies
United States > US
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Summary: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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ISSN:0036-1445
1095-7200
DOI:10.1137/120902434