4
$\begingroup$

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

I am aware of this tutorial using the dual:

https://www.wolfram.com/language/12/convex-optimization/max-cut-problem.html?product=mathematica

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]]; Return[ SemidefiniteOptimization[-Tr[1/4 L . X], Join[Table[ Tr[e[i, n] . X] == 1, {i, 1, n}], {X \[VectorGreaterEqual] 0}], X \[Element] Matrices[{n, n}, Reals], {"PrimalMinimumValue", "PrimalMinimizer"}]]; ];

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

Improve this question
$\endgroup$
4
  • 2
    $\begingroup$ Please include in your question the code that you have tried and what comments you encountered. $\endgroup$ Commented Jun 22, 2021 at 18:16
  • $\begingroup$ Welcome to Mathematica.SE! I hope you will become a regular contributor. To get started, 1) take the introductory tour now, 2) when you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge, 3) remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign, and 4) give help too, by answering questions in your areas of expertise. $\endgroup$ Commented Jun 22, 2021 at 18:17
  • $\begingroup$ xxxx, please take a look at: mathematica.stackexchange.com/help/merging-accounts $\endgroup$ Commented Jun 25, 2021 at 4:20
  • $\begingroup$ Thank you bbgodfrey. Thank you Kuba --- I merged my accounts (sorry for the mess). $\endgroup$ Commented Jun 26, 2021 at 8:04

1 Answer 1

Reset to default
2
$\begingroup$

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}]
Improve this answer
$\endgroup$
1
  • $\begingroup$ Thanks a lot ilian. Yes, that works. I am grateful. $\endgroup$ Commented Jun 26, 2021 at 8:03

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.