||Obtaining Quadratic Models of Noisy Functions
||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.
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.
||Available as Preprint ANL/MCS-P1975-1111, 9/2012
||[PDF from Argonne]|
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"