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Optimal data fitting: a moment approach

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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https://hal.archives-ouvertes.fr/hal-01706850
Contributor : Victor Magron <>
Submitted on : Monday, February 12, 2018 - 12:27:06 PM
Last modification on : Wednesday, September 16, 2020 - 4:46:48 PM

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Jean-Bernard Lasserre, Victor Magron. Optimal data fitting: a moment approach. SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2018, 28 (4), pp.3127-3144. ⟨10.1137/18M1170108⟩. ⟨hal-01706850⟩

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