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mathematical optimization - Kernel crashes during `LinearProgramming`. Can you reproduce it?


Using the code from this answer for a sufficiently large problem setting crashes my kernel. I'll copy/paste the code here:


n = 12;
m = 4;
costs = Range@n/2 // N;


vars = Flatten@{
    Array[x, {n, m}],
    Array[y, m],
    z
    };

constraints = Flatten@{
    Table[Sum[x[i, j], {j, m}] == 1, {i, n}],
    Table[y[j] == Sum[x[i, j] costs[[i]], {i, n}], {j, m}],

    Table[z >= y[j], {j, m}]
    };

bm = CoefficientArrays[Equal @@@ constraints, vars];
solution = LinearProgramming[
   Last@CoefficientArrays[z, vars],
   bm[[2]],
   Transpose@{-bm[[1]], 
     constraints[[All, 0]] /. {Equal -> 0, GreaterEqual -> 1}},
   vars /. {_x -> {0, 1}, (_y | z) -> {0, \[Infinity]}},

   vars /. {_x -> Integers, (_y | z) -> Reals}
   ];


Cases[Pick[vars, solution, 1], x[ij__] :> {ij}];
GroupBy[%, Last -> First] // Values // SortBy[First]

Running this for n=40 yields a result almost instantly, whereas n=60 leads to this


enter image description here


after a minute or so. I am using Mathematica 10.0.1 on Windows 8 64bit. Can you reproduce this behavior? If so, do you have an idea why it is happening?



Small update The kernel crash really appears to be due to LinearProgramming. Everything that is set before or is called within LinearProgramming evaluates basically instantly without issues. Only when solution is evaluated, the kernel crashes - on a Linux x64 it stays alive but Mathematica 10.0.2 freezes and does not return a result even after an hour.




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