D-optimal design for multivariate polynomial regression via the Christoffel function and semidefinite relaxations

2017/03/06 by Yohann de Castro, Fabrice Gamboa, De Castro, Yohann +6
Computer Science · Decision Sciences · #Advanced Multi-Objective Optimization Algorithms #FOS: Mathematics #Optimal Experimental Design Methods #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1703.01777

openalex publication_date 2017/03/06 · openalex created_date 2017/03/16 · openalex updated_date 2026/07/28

Abstract

We present a new approach to the design of D-optimal experiments with multivariate polynomial regressions on compact semi-algebraic design spaces. We apply the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically and approximately the optimal design problem. The geometry of the design is recovered with semidefinite programming duality theory and the Christoffel polynomial.

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