Construction of multivariate polynomial approximation kernels via semidefinite programming

Felix Kirschner; Etienne de Klerk

doi:10.1137/22M1494476

Construction of multivariate polynomial approximation kernels via semidefinite programming

Felix Kirschner, Etienne de Klerk

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Abstract

In this paper we construct a hierarchy of multivariate polynomial approximation kernels for uniformly continuous functions on the hypercube via semidefinite programming. We give details on the implementation of the semidefinite programs defining the kernels. Finally, we show how symmetry reduction may be performed to increase numerical tractability.

Original language	English
Pages (from-to)	513 - 537
Journal	SIAM Journal on Optimization
Volume	33
Issue number	2
DOIs	https://doi.org/10.1137/22M1494476
Publication status	Published - Jun 2023

Keywords

polynomial kernel method
semidefinite programming
symmetry reduction

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10.1137/22M1494476

kernels_JournalVersion_final_submissionAccepted author manuscript, 563 KBLicence: Unspecified
22m1494476Final published version, 723 KBLicence: Taverne

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Construction of multivariate polynomial approximation kernels via semidefinite programming

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Keywords

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