Title: Obtaining Quadratic Models of Noisy Functions
Authors: Aswin Kannan, Stefan Wild
Abstract: When derivatives of a nonlinear objective function are unavailable, many derivative-free optimization algorithms rely on interpolation-based models of the function. But what if the function values are contaminated by noise, as in most of the simulation-based problems typically encountered in this area? We propose to obtain linear and quadratic models by using knowledge of the level of noise in a function. We develop an efficient algorithm for obtaining the model coefficients, and we analyze the properties of the corresponding quadratic program.
Keywords:
Thanks: This work was supported by the Advanced Scientific Computing Research Program, Office of Science, U.S. Department of Energy, under Contract DE-AC02-06CH11357. We are grateful to Jorge Moré for many useful discussions in the course of preparing the manuscript.
Status: Available as Preprint ANL/MCS-P1975-1111, 9/2012
Link: [PDF from Argonne]
BibTeX: 
@techreport{AKSW11,  
    title       = "Obtaining Quadratic Models of Noisy Functions",
    author      = "A. Kannan and S.M. Wild",
    institution = "Mathematics and Computer Science Division",
    month       = "September",    
    year        = "2012",
    number      = "Preprint ANL/MCS-P1975-1111",
    url         = "http://www.mcs.anl.gov/uploads/cels/papers/P1975-1111.pdf"
}
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