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I tried to solve an integer-linear optimization problem but failed. I reduced the failed example to the following:

FindMaximum[{x + y, Element[x , {0, 1}], Element[y , {0, 1}]}, {x, y}]

I got the following error:

FindMaximum::elemc: Unable to resolve the domain or region membership condition x\[Element]{0,1}.

I get the same error when using NMaximize instead of FindMaximum.

What am I doing wrong?

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    $\begingroup$ does NMaximize[{x + y, 0<=x<=1,0<=y<=1}, {x, y}, Integers] work? $\endgroup$
    – kglr
    Commented May 25, 2018 at 11:17
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    $\begingroup$ also FindMaximum[{x + y,x<=1,y<=1, Element[{x,y},Integers]}, {x, y}] $\endgroup$
    – kglr
    Commented May 25, 2018 at 11:21
  • $\begingroup$ @kglr yes, it works! Thanks. $\endgroup$
    – Erel Segal-Halevi
    Commented May 25, 2018 at 11:22
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    $\begingroup$ Voting to close because I think the "elemc" message and the FindMaximum function page hint why OP's command does not work. Although, I might be wrong... $\endgroup$
    – Anton Antonov
    Commented May 25, 2018 at 13:05
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    $\begingroup$ In Mathematica, and unlike in mathematics, {1,2} is not a set, but a list. $\endgroup$
    – AccidentalFourierTransform
    Commented May 25, 2018 at 13:44

1 Answer 1

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NMaximize[{x + y, 0<=x<=1,0<=y<=1}, {x, y}, Integers] (* or *)
FindMaximum[{x + y,x<=1,y<=1, Element[{x,y},Integers]}, {x, y}]

both give

{2., {x -> 1, y -> 1}}

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    $\begingroup$ Thanks. I still do not understand why my command did not work, but this solved my problem. $\endgroup$
    – Erel Segal-Halevi
    Commented May 26, 2018 at 17:49

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