Miles, I have successfully installed JuMP and GLPKMathProgInterface on
Windows 32-bit.
Your code works very well, this is really awesome !! However the result is
not as precise as the one given by *GLPK.exact*.
using JuMP
mu = [1/7, 2/7, 4/7]
nu = [1/4, 1/4, 1/2]
n = length(mu)
m = Model()
@defVar(m, p[1:n,1:n] >= 0)
@setObjective(m, Min, sum{p[i,j], i in 1:n, j in 1:n; i != j})
for k in 1:n
@addConstraint(m, sum(p[k,:]) == mu[k])
@addConstraint(m, sum(p[:,k]) == nu[k])
end
solve(m)
julia> println("Optimal objective value is:", getObjectiveValue(m))
Optimal objective value is:0.10714285714285715
julia> 3/28
0.10714285714285714
Le jeudi 10 avril 2014 01:28:41 UTC+2, Miles Lubin a écrit :
>
> When we have a simplex solver (either in Julia or external) that supports
> rational inputs, we could consider making this work with JuMP, but for now
> JuMP stores all data as floating-point as well.
>
> Stephane, nice work. LP definitely needs more exposure in the probability
> community. Please please write your LPs algebraically, there's really no
> excuse not to do this in Julia when your original model is in this form.
>
> Compare this:
>
> using JuMP
> m = Model()
> @defVar(m, p[1:n,1:n] >= 0)
> @setObjective(m, Max, sum{p[i,j], i in 1:n; i != j})
>
> for k in 1:n
> @addConstraint(m, sum(p[k,:]) == μ[k])
> @addConstraint(m, sum(p[:,k]) == ν[k])
> end
> solve(m)
> println("Optimal objective value is:", getObjectiveValue(m))
>
>
> with the matrix gymnastics that you had to do to use the low-level GLPK
> interface. Writing down a linear programming problem shouldn't be that
> hard! (Note: I haven't tested that JuMP code).
>
> Miles
>
>
>
> On Wednesday, April 9, 2014 11:18:26 PM UTC+1, Carlo Baldassi wrote:
>>
>>
>>
>> About GLPK.exact it is not possible to get the rational number 3/28
>>> instead of a decimal approximation ?
>>>
>>
>> No, unfortunately. Also, for that to happen/make sense, you'd also need
>> to be able to pass all the *inputs* as exact rational values, i.e. as
>> "1//7" instead of "1/7". This would be possible if we had a native generic
>> Julia linear programming solver, but it's not possible with GLPK, which can
>> only use exact arithmetic internally.
>>
>
