I am not really a math guru myself, but I know that many estimation or approximation problems can be reformulated as minimizing the rank of a matrix. Although that is really hard, we can try to minimize the nuclear norm instead, which turns out to be a convex optimization problem that is easier to solve.
Let's say I have a sparse matrix X which I need to fill and somehow I've found the minimal nuclear norm. How can I impute the missing values now? And how the whole idea of minimizing the rank relate to that? Can you provide me with a simple(visual, if possible) example, please?