I am trying to make the following code work:

M = {{x11, x12, x13}, {x21, x22, x23}, {x31, x32, x33}};
  VectorGreaterEqual[{M, 0}, {"SemidefiniteCone", 3}], 

However, it just stops and does nothing. Essentially, the SDP problem would consist on finding the first matrix $M$ that is positive semidefinite.

  • 1
    $\begingroup$ Does VectorGreaterEqual[{M, 0} impliy semidefiniteness of M? $\endgroup$ – user64494 Oct 12 '20 at 13:08
  • $\begingroup$ I think it does, at least that is the translation of the symbol appearing in the reference. reference.wolfram.com/language/ref/… $\endgroup$ – bdt Oct 12 '20 at 13:22
  • $\begingroup$ Indeed, this quits the kernel. Must be a memory issue. This must not happen. Please contact Wolfram Support about this. $\endgroup$ – Henrik Schumacher Oct 12 '20 at 13:53

Up to the documentation,

The matrices Subscript[a, j] must be symmetric n *n matrices.

Therefore, M should be changed to become a symmetric matrix. The following works.

M = {{x11, x12, x13}, {x12, x22, x23}, {x13, x23, x33}};
SemidefiniteOptimization[1, VectorGreaterEqual[{M, 0}, {"SemidefiniteCone", 3}], {x11, x12, x13, 
x22, x23, x33}]
(*{x11 -> 20.9077, x12 -> 0., x13 -> 0., x22 -> 20.9077, x23 -> 0., x33 -> 20.9077}*)

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.