# Reformulating Logarithmic Objective Function for Gurobi in Julia with JuMP
**URL:** https://discourse.julialang.org/t/reformulating-logarithmic-objective-function-for-gurobi-in-julia-with-jump/121961
**Category:** Optimization (Mathematical)
**Tags:** question, gurobi, convex-optimization
**Created:** [October 29, 2024, 9:35pm UTC](https://discourse.julialang.org/t/reformulating-logarithmic-objective-function-for-gurobi-in-julia-with-jump/121961 "2024-10-29T21:35:47Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@Beyza\_Aydin](https://discourse.julialang.org/u/Beyza_Aydin)
#### Post date: [October 29, 2024, 9:35pm UTC](https://discourse.julialang.org/t/reformulating-logarithmic-objective-function-for-gurobi-in-julia-with-jump/121961/1 "2024-10-29T21:35:47Z")
Hi,
I’m working on an optimization problem in Julia where I need to maximize a logarithmic objective function (maximize sum of logs ):
` @objective(model, Max, sum(alp[i] * log( p[i]) for i in 1:n))`
where alp is vector of ones and p is a variable.
However, I’ve found that Gurobi doesn’t support logarithmic functions directly, and my attempts to access the C API using `grb = backend(model)` resulted in a “backend couldn’t be found” error.
Could anyone suggest how I might reformulate this objective in a way compatible with Gurobi, or provide guidance on using the Gurobi C API in Julia to handle this type of problem? Any advice on alternative approaches would also be much appreciated.
Thank you!
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [October 29, 2024, 9:48pm UTC](https://discourse.julialang.org/t/reformulating-logarithmic-objective-function-for-gurobi-in-julia-with-jump/121961/2 "2024-10-29T21:48:20Z")
Hi @Beyza_Aydin, welcome to the forum 😄
Here you go:
```julia
julia> using JuMP
julia> import Gurobi
julia> n = 3
3
julia> model = direct_model(Gurobi.Optimizer())
A JuMP Model
├ mode: DIRECT
├ solver: Gurobi
├ objective_sense: FEASIBILITY_SENSE
├ num_variables: 0
├ num_constraints: 0
└ Names registered in the model: none
julia> @variable(model, p[i in 1:n] == i)
3-element Vector{VariableRef}:
p[1]
p[2]
p[3]
julia> @variable(model, log_p[1:n])
3-element Vector{VariableRef}:
log_p[1]
log_p[2]
log_p[3]
julia> grb = backend(model)
sense : minimize
number of variables = 0
number of linear constraints = 0
number of quadratic constraints = 0
number of sos constraints = 0
number of non-zero coeffs = 0
number of non-zero qp objective terms = 0
number of non-zero qp constraint terms = 0
julia> column(x::VariableRef) = Gurobi.c_column(grb, index(x))
column (generic function with 1 method)
julia> for i in 1:n
Gurobi.GRBaddgenconstrLog(grb, "log(p[$i])", column(p[i]), column(log_p[i]), "")
end
julia> optimize!(model)
Gurobi Optimizer version 11.0.3 build v11.0.3rc0 (mac64[x86] - Darwin 23.5.0 23F79)
CPU model: Intel(R) Core(TM) i5-8259U CPU @ 2.30GHz
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 0 rows, 6 columns and 0 nonzeros
Model fingerprint: 0xe8e701e1
Model has 3 general constraints
Variable types: 6 continuous, 0 integer (0 binary)
Coefficient statistics:
Matrix range [0e+00, 0e+00]
Objective range [0e+00, 0e+00]
Bounds range [1e+00, 3e+00]
RHS range [0e+00, 0e+00]
Presolve removed 0 rows and 6 columns
Presolve time: 0.00s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)
Solution count 1: 0
Optimal solution found (tolerance 1.00e-04)
Best objective 0.000000000000e+00, best bound 0.000000000000e+00, gap 0.0000%
User-callback calls 90, time in user-callback 0.00 sec
julia> value.(p)
3-element Vector{Float64}:
1.0
2.0
3.0
julia> value.(log_p)
3-element Vector{Float64}:
0.0
0.6931471805599453
1.0986122886681098
julia> log.(value.(p))
3-element Vector{Float64}:
0.0
0.6931471805599453
1.0986122886681098
```
---
### Author:  [@Beyza\_Aydin](https://discourse.julialang.org/u/Beyza_Aydin)
#### Post date: [October 30, 2024, 2:36pm UTC](https://discourse.julialang.org/t/reformulating-logarithmic-objective-function-for-gurobi-in-julia-with-jump/121961/3 "2024-10-30T14:36:42Z")
Thank you very much! My code is finally working 🙂
I guess the important part is to `import Gurobi`, and not using `using Gurobi`
I also added this objective function:
```julia
@objective(model, Max, sum(alp.*log_p))
```
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [October 30, 2024, 8:25pm UTC](https://discourse.julialang.org/t/reformulating-logarithmic-objective-function-for-gurobi-in-julia-with-jump/121961/4 "2024-10-30T20:25:20Z")
> I guess the important part is to `import Gurobi` , and not using `using Gurobi`
This should have nothing to do with it. If you use `import Gurobi`, then you need to prefix all calls to Gurobi with `Gurobi.`. If you use `using Gurobi`, then all of the `GRBxxx` symbols are brought into scope and you can use `GRBaddgenconstrLog` without `Gurobi.`.