Can someone give a workaround and/or explanation why Problem 1/Problem 2 fail to solve through SemidefiniteOptimization
? Problem 3 works. (I'm using 12.1.0 on Mac). The main difference is that Problem 1+2 use diagonal matrix constraint, whereas Problem 3 matrix constraint has no 0's. I could solve them using other meanswithout calling SemidefiniteOptimization
, but prefer to have a single toolsolution to cover a wide range of cases.
$$ \text{min}_{A,x} x $$ Subject to $$ I \succ A \succ -I\\ x I \succ -\sum_i^{d^2} V_i' A V_i \\ $$
Interestingly, substituting random matrices for $V_i$'s, I get the expected result out of SemidefiniteProgramming
. For some reason Mathematica has more trouble with diagonal matrix constraints than random constraints