D-optimal design for multivariate polynomial regression via the Christoffel function and semidefinite relaxations
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.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2017
- DOI:
- 10.48550/arXiv.1703.01777
- arXiv:
- arXiv:1703.01777
- Bibcode:
- 2017arXiv170301777D
- Keywords:
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- Mathematics - Statistics Theory;
- Mathematics - Optimization and Control