Wolfram|Cloud memory limit exceeded

Question

I have some formulas from a paper (Provably Manipulation-Resistant Reputation Systems) that I would like to run 3 times (with different nummbers).

Therefore, I wrote a small programm that now finally works ... and bam:

This computation has exceeded the memory limit for your plan

I didn't know something like this could occur.

Is there anything I can do to improve my code so that it runs to completion?

Formulas:

This is my code (first time coding with Wolfram|Cloud):

unr =  4;
lnr =  3;
size = unr * lnr;
eps =  0.2;

e = SparseArray[{{2, 3} -> -1}, {size,size}];
n = Array[f , {size,size}];

bounds = (If[0 <= # <= 1, True, Throw[False], Throw[False]])&;
checkLessEquals = (Catch[Map[bounds, #, {2}]; Throw[True]])&;

prod = (Total[#1*#2, 2])&;

ArgMax[
  {eps *  prod[e, n] + Log[Det[n+IdentityMatrix[size]]], 
   checkLessEquals[n] && PositiveDefiniteMatrixQ[n]}, 
  Flatten[n]]

Answer 1

You can test for the conditions explicitly:

ve = Array[v, {size}];
ArgMax[{(eps*prod[e, n] + Log[Det[n + IdentityMatrix[size]]]), 
0 < # < 1 & /@ Flatten@n, ({ve}.n.ve) > 0}, Flatten[{n, ve}]]
Chop[%, 10^-8]

1., 0, 1., 1., 0, 0, 1., 1., 0, 1., 1., 0, 0, 1., 1., 0, 0, 0, 0, 0, 1., 1., 1., 1., 1., 0, 1., 0, 1., 1., 1., 1., 0, 0, 0, 1., 1.4288, 0.403799, -0.37193, 0.742415, -0.39883, -0.0280605}