The suppport reduction algorithm for computing nonparametric function   estimates in mixture models
  Vertex direction algorithms have been around for a few decades in the experimental design and mixture models literature. We briefly review this type of algorithm and describe a new member of the family: the support reduction algorithm. The support reduction algorithm is applied to the problem of computing nonparametric estimates in two inverse problems: convex density estimation and the Gaussian deconvolution problem. Usually, VD algorithms solve a finite dimensional (version of the) optimization problem of interest. We introduce a method to solve the true infinite dimensional optimization problem. 
Piet Groeneboom (Delft University), Geurt Jongbloed (Vrije   University), Jon A. Wellner (University of Washington)