graph theory - Quadratic programming in Mathematica -

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i'm looking @ quadratic relaxation of maximum independent set problem (p.22 here), , found findmaximum fails every graph try, unless give optimal solution starting point. these quadratic programmes have 10-20 variables, expect them solvable.

  1. is there way make mathematica solve such quadratic programmes?
  2. is there quadratic programming package that's easy call within mathematica?

here's example of failing findmaximum, followed working findmaximum initialized @ solution

setupquadratic[g_graph] := (    ag = adjacencymatrix[g];    = identitymatrix[length@vertexlist@g] - ag;    cons = , @@ table[0 <= x[v] <= 1, {v, vertexlist@g}];    vars = x /@ vertexlist[g];    indset = findindependentvertexset@g;    xopt = array[boole[memberq[indset, #]] &, {length@vertexlist@g}];    );  g = graphdata[{"cubic", {10, 11}}]; setupquadratic[g]; findmaximum[{vars.a.vars, cons}, vars] findmaximum[{vars.a.vars, cons}, thread[{vars, xopt}]]

here other graphs tried

{"dodecahedralgraph", "fruchtgraph", "truncatedprismgraph", \ "truncatedtetrahedralgraph", {"cubic", {10, 2}}, {"cubic", {10,     3}}, {"cubic", {10, 4}}, {"cubic", {10, 6}}, {"cubic", {10,     7}}, {"cubic", {10, 11}}, {"cubic", {10, 12}}, {"cubic", {12,     5}}, {"cubic", {12, 6}}, {"cubic", {12, 7}}, {"cubic", {12,     9}}, {"cubic", {12, 10}}}

might try method shown in package located here. see problem 8

daniel lichtblau wolfram research


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