Timeline for Minimize trace of inverse of convex combination of matrices.

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Jun 21, 2011 at 21:50	comment	added	Suvrit		If you just want to approximate the solution that can be done easily---one way is, as you mention, MM; more simply, you can just lower-bound the objective, and then solve a linear problem. However, I did not mention that, because it leads to a "trivial" solution. As for "minimization", since the leading singular value (here eigenvalue) is a convex function, yes, you do want to minimize, not maximize.
Jun 21, 2011 at 14:01	comment	added	jvdillon		Hi Suvrit--thanks for taking the time to think about this. First question: Does minimizing the L2 norm make sense? Perhaps you mean to maximize this? Anyway, that's an easy enough fix. Second question: Regarding SDP approaches: I have toyed with SDP solvers (and similar formulations as you have given; I also tried logdet) for toy models but it is far too unscalable to be useful. I would much prefer an approximate solution. Do you know of techniques to approximate SDP problems? (I am imagining a majorization/minimization procedure.)
Jun 21, 2011 at 5:38	comment	added	Brian Borchers		you'll need to do this for $c=e_{1}$, $c=e_{2}$, ..., so you'll end up with a block diagonal SDP constraint.
Jun 21, 2011 at 2:50	history	answered	Suvrit	CC BY-SA 3.0