Consider the following illumination problem: given a stage represented by a line segment and a set of lightsources represented by a set of points in the plane, assign powers to the lightsources such that every point on the stage receives a sufficient amount -- let's say one unit -- of light while minimizing the overall power consumption. By assuming that the amount of light arriving from a fixed lightsource decreases rapidly with the distance from the lightsource, this becomes
an interesting optimization problem.
We examine the simple problem introduced above and presents different solutions, based on convex optimization, discretization and linear programming, as well as a purely combinatorial approximation algorithm.