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arXiv · 2101.08080

A Damped Newton Algorithm for Generated Jacobian Equations

Anatole Gallouët·Quentin Merigot·Boris Thibert
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Abstract

Generated Jacobian Equations have been introduced by Trudinger [Disc. cont. dyn. sys (2014), pp. 1663-1681] as a generalization of Monge-Amp{\`e}re 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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BibTeXRIS

Anatole Gallouët, Quentin Merigot, Boris Thibert. 2021-01-20. A Damped Newton Algorithm for Generated Jacobian Equations. https://arxiv.org/abs/2101.08080

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