The maximum entropy method on the mean: Applications to linear programming and superresolution

In this paper, the authors give two different results. They propose new methods to solve classical optimization problems in linear programming. The authors also obtain precise quantitative results for the superresolution phenomenon, as observed earlier by practical searches on specific algorithms. The common background of the work is the generalized moment problem, which is known to be connected with linear programming and superresolution. The authors describe the maximum Entropy Method on the Mean that provides solution to the problem and leads to computational criteria to decide the existence of solutions or not.