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.

翻译：特鲁丁杰[Disc. cont. dyn. sys(2014年),pp.1663-1681]作为最佳运输中产生的蒙古-安普斯(Amp ⁇ e)等式的概括性,引入了生成的雅各克方程式。在本文中,我们引入并研究一种在半分立环境中解决这些等式的摇篮式牛顿算法,这意味着问题涉及的两种措施之一得到有限的支持,而另一措施则是绝对持续的。我们还将这种算法在数字上应用到近场平行的非成形问题产生的相联性问题。