That makes sense, at least as long as the vector- or matrix-valued objective behaves somewhat. I guess I've been using this all along (with transformations to enforce proper behavior) for matrix and tensor completion anyways... Hmm. I just didn't implement it terribly elegantly!

Now that I think about it, all of the methods I've ever seen for matrix-valued time series fits (i.e. multiple measurements at multiple sites per time point) are Bayesian. That's about the most irreducible constrained optimization problem I can think of in this setting.