使用 julia 和 gurobi 的二次约束 MIQP [英] Quadratically constrained MIQP with julia and gurobi

问题描述

这是试图回答以下问题:https://matheducators.stackexchange.com/questions/11757/small-data-sets-with-integral-sample-standard-deviations

This is an attempt to answer the following question: https://matheducators.stackexchange.com/questions/11757/small-data-sets-with-integral-sample-standard-deviations

因此，以下代码的目的是查找具有整数标准差的小型数据集的示例.这可以表述为一个二次约束的混合整数二次程序，所以我尝试使用来自 Julia 的 Gurobin.以下是我的代码:

So the intent of the following code is to find examples of small datasets with integer standard deviation. That can be formulated as a quadratically constrained mixed integer quadratic program, so I try to use Gurobin from Julia. Following is my code:

using JuMP  
using Gurobi

m = Model(solver = GurobiSolver() )
@variable(m,  0<= x[1:20] <= 100,  Int)
@variable(m,  Gj,  Int)
@constraint(m,  Gj == sum(x[1:20])/20 )
@variable(m,  Var,  Int)
@constraint(m,  Var == sum( (x[1:20]-Gj).^2/19) )
@variable(m,  sd,  Int)
@constraint(m, sd * sd == Var)
### We need some restrictions to avoid all equal, < or zero,  solutions:
@constraint(m,  sd >= 5)
@objective(m, Min, sd)

print(m)

status = solve(m)

println("Objective value: ", getobjectivevalue(m) )

x = getvalue(x)

运行此结果:

ERROR: Gurobi.GurobiError(10021, "Quadratic equality constraints")
Stacktrace:
 [1] optimize(::Gurobi.Model) at /home/kjetil/.julia/v0.6/Gurobi/src/grb_solve.jl:7
 [2] optimize!(::Gurobi.GurobiMathProgModel) at /home/kjetil/.julia/v0.6/Gurobi/src/GurobiSolverInterface.jl:294
 [3] #solve#101(::Bool, ::Bool, ::Bool, ::Array{Any,1}, ::Function, ::JuMP.Model) at /home/kjetil/.julia/v0.6/JuMP/src/solvers.jl:173
 [4] solve(::JuMP.Model) at /home/kjetil/.julia/v0.6/JuMP/src/solvers.jl:148

有什么想法吗?

推荐答案

像 Gurobi Optimizer 这样的数学编程求解器无法求解具有二次等式约束的模型.以下是 Gurobi Optimizer 可以解决的约束类型.要使用 Gurobi Optimizer 求解模型，您必须将约束转换为其中一种形式，例如二次不等式约束.

A math programming solver like Gurobi Optimizer cannot solve models with quadratic equality constraints. Here are the types of constraints that Gurobi Optimizer can solve. To solve your model using Gurobi Optimizer, you must transform your constraints into one of these forms, such as quadratic inequality constraints.

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