The paper gives a novel SVD-free variational formulation of the Schatten-p matrix quasi-norm for p in (0,1), including an analysis of the problems caused by local minima and how to avoid them. The method is tested briefly on Schatten-norm matrix completion but the main emphasis of the paper is theoretical and the empirical improvements achieved relative to the directly competing FGSR method are limited. Two reviewers scored this above threshold, one below. In discussion the negative reviewer agreed that the method's ability to deal with p<1 is valuable, but still felt that the advance was too limited for acceptance. On balance the AC and SAC decided that the positive points were sufficient for acceptance given the importance of low-p Schatten norms for a range of ML methods. In the final paper, the discussion of the advantages of the new approach relative to FGSR needs to be strengthened.