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HAL-LAAS Open Archive Laboratory for Analysis and Architecture of Systems |  |
Journal articles
Approximate Optimal Designs for Multivariate Polynomial Regression
Abstract : We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically the approximate optimal design problem. The geometry of the design is recovered via semidefinite programming duality theory. This article shows that the hierarchy converges to the approximate optimal design as the order of the hierarchy increases. Furthermore, we provide a dual certificate ensuring finite convergence of the hierarchy and showing that the approximate optimal design can be computed numerically with our method. As a byproduct, we revisit the equivalence theorem of the experimental design theory: it is linked to the Christoffel polynomial and it characterizes finite convergence of the moment-sum-of-square hierarchies.
Cited literature [24 references]
https://hal.laas.fr/hal-01483490
Contributor : Didier Henrion <>
Submitted on : Tuesday, October 17, 2017 - 10:41:26 AM
Last modification on : Thursday, June 10, 2021 - 3:08:42 AM
Long-term archiving on: : Thursday, January 18, 2018 - 12:42:10 PM
Contributor : Didier Henrion <>
Submitted on : Tuesday, October 17, 2017 - 10:41:26 AM
Last modification on : Thursday, June 10, 2021 - 3:08:42 AM
Long-term archiving on: : Thursday, January 18, 2018 - 12:42:10 PM
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