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A damped Newton algorithm for generated Jacobian equations

Abstract : Generated Jacobian Equations have been introduced by Trudinger [Disc. cont. dyn. sys (2014), pp. 1663-1681] as a generalization of Monge-Ampère equations arising in optimal transport. In this paper, we introduce and study a damped Newton algorithm for solving these equations in the semi-discrete setting, meaning that one of the two measures involved in the problem is finitely supported and the other one is absolutely continuous. We also present a numerical application of this algorithm to the near-field parallel refractor problem arising in non-imaging problems.
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https://hal.archives-ouvertes.fr/hal-03116036
Contributor : Boris Thibert <>
Submitted on : Wednesday, January 20, 2021 - 9:06:28 AM
Last modification on : Wednesday, March 10, 2021 - 3:04:04 PM

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  • HAL Id : hal-03116036, version 1
  • ARXIV : 2101.08080

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Anatole Gallouët, Quentin Merigot, Boris Thibert. A damped Newton algorithm for generated Jacobian equations. [Research Report] Université Grenoble Alpes; Université Paris Sud. 2021. ⟨hal-03116036⟩

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