# Stuck with infeasibility certificates in JuMP.jl
**URL:** https://discourse.julialang.org/t/stuck-with-infeasibility-certificates-in-jump-jl/102210
**Category:** Optimization (Mathematical)
**Tags:** jump
**Created:** [July 28, 2023, 7:38pm UTC](https://discourse.julialang.org/t/stuck-with-infeasibility-certificates-in-jump-jl/102210 "2023-07-28T19:38:43Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@sstroemer](https://discourse.julialang.org/u/sstroemer)
#### Post date: [July 28, 2023, 7:38pm UTC](https://discourse.julialang.org/t/stuck-with-infeasibility-certificates-in-jump-jl/102210/1 "2023-07-28T19:38:44Z")
I’m trying to work with infeasibility certificates and different solvers.
MWE using `GLPK`:
```julia
using JuMP
import HiGHS, Gurobi, GLPK
model = JuMP.Model(() -> GLPK.Optimizer(; want_infeasibility_certificates = true))
@variable(model, x; lower_bound=0, upper_bound=10)
@variable(model, θ)
@objective(model, FEASIBILITY_SENSE, x + θ)
optimize!(model)
result_count(model) # 1
JuMP.value(x) # 0.0
JuMP.value(θ) # 0.0
```
This seems to “work” (but just by using `want_infeasibility_certificates`, not depending on `FEASIBILITY_SENSE`, since it works with `Min` as well). Using `HiGHS` fails though:
```julia
using JuMP
import HiGHS, Gurobi, GLPK
model = JuMP.Model(HiGHS.Optimizer)
@variable(model, x; lower_bound=0, upper_bound=10)
@variable(model, θ)
@objective(model, FEASIBILITY_SENSE, x + θ)
optimize!(model)
result_count(model) # 0
JuMP.value(x) # ERROR: ...
JuMP.value(θ) # ERROR: ...
```
* * *
Notes:
- `print(model)` “correctly” shows the objective as `Feasibility`
- `objective_function(model)` still prints `x + θ`; does that mean that this is still being passed to the solver? I assume yes, since using `@objective(model, FEASIBILITY_SENSE, x)` influences which feasible solution the solver returns, depending on whether I pass `x` or `-x` as "objective. If so, is there an advantage of doing that (instead of passing any constant as objective function), besides that it enables us to later use `set_objective_sense(...)` to change it (which is nice for not rebuilding the objective function, but then maybe objective\_function(…)`should check the`ObjectiveSense`)?
- Similar to `want_infeasibility_certificates = true` for `GLPK` using `set_optimizer_attribute(model, "InfUnbdInfo", 1)` for Gurobi works, again independent of `FEASIBILITY_SENSE`.
- I assume it only fails for HiGHS, since I couldn’t find a solver specific attribute to set there.
Sticking to [the documentation](https://jump.dev/JuMP.jl/stable/moi/background/infeasibility_certificates/), I tried checking the `TerminationStatus` as well as the `PrimalStatus`:
GLPK:
`Termination status : DUAL_INFEASIBLE | Primal status : NO_SOLUTION`
Gurobi:
`Termination status : DUAL_INFEASIBLE | Primal status : INFEASIBILITY_CERTIFICATE`
HiGHS:
`Termination status : DUAL_INFEASIBLE | Primal status : NO_SOLUTION`
which indicates probably also that the `InfUnbdInfo` setting for Gurobi is properly detected, while `want_infeasibility_certificates` is not (so I can’t distinguish between a successful run and one that failed)?
* * *
So, maybe I’m looking for the wrong thing: Is there any solver-independent way to set the “I want infeasibility certificates” attribute (e.g. failing for solvers that do not support that, or just ignoring it and properly indicating that in the `PrimalStatus`).
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [July 31, 2023, 11:08pm UTC](https://discourse.julialang.org/t/stuck-with-infeasibility-certificates-in-jump-jl/102210/2 "2023-07-31T23:08:16Z")
In general, there is no guarantee that a solver will find an infeasibility certificate for an infeasible or unbounded problem. For example, in some cases that can prove infeasibility during preserve without generating a certificate.
If you have a solver that doesn’t return a certificate, you’ll generally need to change some solver-specific settings, the most common being to disable the solver’s presolve. For HiGHS, try setting `"presolve"` to `"off"`: [List of options · HiGHS Documentation](https://ergo-code.github.io/HiGHS/dev/options/definitions/#presolve).
Also, I need to double check what’s going on with explicitly providing `FEASIBILITY_SENSE` and an objective. The definition of `FEASIBILITY_SENSE` is that the model does not have an objective, so it’s likely that the solver is ignoring the objective. JuMP should probably throw an error here.