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arXiv · 1802.03259

Optimal data fitting: a moment approach

Jean-Bernard Lasserre·Victor Magron
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Abstract

We propose a moment relaxation for two problems, the separation and covering problem with semi-algebraic sets generated by a polynomial of degree d. We show that (a) the optimal value of the relaxation finitely converges to the optimal value of the original problem, when the moment order r increases and (b) after performing some small perturbation of the original problem, convergence can be achieved with r=d. We further provide a practical iterative algorithm that is computationally tractable for large datasets and present encouraging computational results.

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Jean-Bernard Lasserre, Victor Magron. 2018-02-09. Optimal data fitting: a moment approach. https://arxiv.org/abs/1802.03259

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