Efficiently Retrieving Variable Values after Gurobi optimization with JuMP

Specific Domains Optimization (Mathematical)
15

Actually I knew this package Dualization.jl.
But my dream is different, being something like a code generator (e.g. ChatGPT).
If a segment of JuMP code of the primal formulation is input into it, then it can print the JuMP code of the dual formulation in julia REPL, then I can copy it to my text editor. (Sounds a bit advanced, but it is bound to be way more flexible—thus usable)
For example, I input the following code

function stage2_problem_primal(z, d)
    JuMP.@variable(st2, x[i = 1:3, j = 1:3] >= 0)
    JuMP.@constraint(st2, DI[i = 1:3], z[i]         >= sum(x[i, :]))
    JuMP.@constraint(st2, DJ[j = 1:3], sum(x[:, j]) >= d[j]        )
    JuMP.@objective(st2, Min, sm(C_x, x))
end

Then an oracle gives me the following code at julia REPL

function stage2_problem_dual(z, d)
    JuMP.@variable(Dst2, DI[i = 1:3] >= 0)
    JuMP.@variable(Dst2, DJ[j = 1:3] >= 0)
    JuMP.@constraint(Dst2, x[i = 1:3, j = 1:3], C_x[i, j] + DI[i] - DJ[j] >= 0)
    JuMP.@objective(Dst2, Max, sm(DJ, d) - sm(DI, z))
end

The sm function is dot, see here.
As you can see there are strong correspondence among the two:

  1. The primal is Min, then the dual is Max.
  2. The primal’s variables become the dual’s constraint, whereas the primal’s constraint become the dual’s variable
  3. If we do not write “<=” constraint, and do not use “<= 0” variables in the primal side, then the same appearance will be on the dual side.