二次约束MIQP与Julia和Gurobi [英] Quadratically constrained MIQP with julia and gurobi

问题描述

这是尝试回答以下问题的尝试: 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.可以将其表示为二次约束混合整数二次程序，因此我尝试使用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)

运行此结果将导致:

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. 这是Gurobi Optimizer可以解决的约束类型.要使用Gurobi Optimizer求解模型，必须将约束转换为以下形式之一，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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