  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.
