How could one formulate the primal SDP for MaxCut in Mathematica.

I am aware of this tutorial using the dual:


Thank you.

Edit to add further information:

What I tried (there LaplacianMatrix and e are functions from the dual example):

MCSDPPrimalValueAndMinimizer[graph_?GraphQ] := 
  Module[{L = LaplacianMatrix[graph], n},
   n = Dimensions[L][[1]];
    SemidefiniteOptimization[-Tr[1/4 L . X], 
       Tr[e[i, n] . X] == 1, {i, 1, n}], {X \[VectorGreaterEqual] 0}],
      X \[Element] Matrices[{n, n}, Reals], {"PrimalMinimumValue", 

However, the values it returns are pretty off even for even order complete graphs --- they should match the optimal values of their maxcuts.

  • 2
    $\begingroup$ Please include in your question the code that you have tried and what comments you encountered. $\endgroup$
    – bbgodfrey
    Jun 22 at 18:16
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    – bbgodfrey
    Jun 22 at 18:17
  • $\begingroup$ xxxx, please take a look at: mathematica.stackexchange.com/help/merging-accounts $\endgroup$
    – Kuba
    Jun 25 at 4:20
  • $\begingroup$ Thank you bbgodfrey. Thank you Kuba --- I merged my accounts (sorry for the mess). $\endgroup$
    – xxxx
    Jun 26 at 8:04

More of a comment, but this looks almost correct, the main issue is that instead of

VectorGreaterEqual[{X, 0}]

you may want to use

VectorGreaterEqual[{X, 0}, {"SemidefiniteCone", n}]
  • $\begingroup$ Thanks a lot ilian. Yes, that works. I am grateful. $\endgroup$
    – xxxx
    Jun 26 at 8:03

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