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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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Dates and versions

hal-03116036 , version 1 (20-01-2021)

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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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