Non-imaging optics consists in optimizing the trajectory of the light from a source to a target without trying to form an image of the source on the target. Some non-imaging optic problems can be translated into Optimal Transport problems in a semi-discrete setting, meaning that the source is a continuous domain and the target is a finite set of points. Other problems of non-imaging optics can sometimes be rewritten into a slightly more global form than optimal transport, which we call Generated Jacobian Equations. In this presentation I will first introduce semi-discrete Optimal Transport. Then I will present two non-imaging optics problem, one of which is O.T. and the other a Generated Jacobian equation which are some "generalization" of optimal transport. The main goal is to present a Newton algorithm to solve these Generated Jacobian Equations, which was adapted from an existing algorithm to solve optimal transport problems. Finally we will detail the main lines of the proof of convergence of this algorithm.
