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## Re: [Help-glpk] First element of the set

**From**: |
xypron |

**Subject**: |
Re: [Help-glpk] First element of the set |

**Date**: |
Thu, 22 Oct 2009 10:05:32 -0700 (PDT) |

Hello
>*> have a set MBC.*
>*> Now I need the restriktion, y[x]=0 where x is just the first element of*
>*> the MBC. *
sets in GLPK are unordered. Hence the first element cannot be accessed. Of
cause you could define a parameter with the value of the first element.
Determining a set containing the smallest element of a given set is
possible.
See example below.
Best regards
Xypron
# some set
set S;
# set of the smallest element in S
# GLPK is inefficient here, needing O(n^2) time!
set F := setof{ s in S : forall{u in S} s <= u } s;
# variable
var y{s in S}, >= 0, <=1;
# some objective
maximize obj :
sum{s in S} y[s];
# constraint for the smallest element in S
s.t. c1{s in F} :
y[s] = 0;
# display constraint
display c1;
# initialization
data;
set S := the quick brown fox jumps over a lazy dog;
--
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