# EAGO does not identify infeasbility of constraints in "easy" problem

**URL:** <https://discourse.julialang.org/t/eago-does-not-identify-infeasbility-of-constraints-in-easy-problem/90820>\
**Category:** Optimization (Mathematical)\
**Created:** [November 25, 2022, 4:54pm UTC](https://discourse.julialang.org/t/eago-does-not-identify-infeasbility-of-constraints-in-easy-problem/90820 "2022-11-25T16:54:10Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![recallme](https://avatars.discourse-cdn.com/v4/letter/r/a87d85/32.png) [@recallme](https://discourse.julialang.org/u/recallme)\
**Post date:** [November 25, 2022, 4:54pm UTC](https://discourse.julialang.org/t/eago-does-not-identify-infeasbility-of-constraints-in-easy-problem/90820/1 "2022-11-25T16:54:10Z")

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Hi,

in the below problem I defined two constraints for which it is trivial to show analytically that they cannot be satisfied at the same time. However, the code takes lots of time and does not give back a clear unfeasibility certificate. **Why is this?** For other problems where I cannot show infeasibility analytically, the same code with other constraints works perfect.

Any help is appreciated.

```julia
using JuMP, EAGO
m = Model(EAGO.Optimizer)
# Define bounded variables
@variable(m, 10^(-6)<=c0<=10)
@variable(m, 10^(-6)<=c1<=10)
@variable(m, 1<=z0<=10)
@variable(m, 1<=z1<=10)
@variable(m, 10^(-6)<=v<=100)
# Define nonlinear constraints
@NLconstraint(m, e4, (18 * c1 - v^2 * (1 + z1 ) ) * (18 * c1 - v^2 * z1 ) <= -1 )
@NLconstraint(m, e5, (-18 * c1 + v^2 * (1 + z1 ))<= -1 )
# Define nonlinear objective
@NLobjective(m, Max, 0)
# Solve the optimization problem
optimize!(m)

```

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**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [November 26, 2022, 5:01am UTC](https://discourse.julialang.org/t/eago-does-not-identify-infeasbility-of-constraints-in-easy-problem/90820/2 "2022-11-26T05:01:33Z")

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> However, the code takes lots of time and does not give back a clear unfeasibility certificate. **Why is this?**

Detecting infeasibility in problems like this is hard. Solvers don’t work for every problem, even simple ones.

You could try opening an issue: [Issues · PSORLab/EAGO.jl · GitHub](https://github.com/PSORLab/EAGO.jl/issues). I’m sure the developers would appreciate examples where their code could be improved.

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<div class="post-metadata">

**Author:** ![recallme](https://avatars.discourse-cdn.com/v4/letter/r/a87d85/32.png) [@recallme](https://discourse.julialang.org/u/recallme)\
**Post date:** [November 26, 2022, 1:37pm UTC](https://discourse.julialang.org/t/eago-does-not-identify-infeasbility-of-constraints-in-easy-problem/90820/3 "2022-11-26T13:37:40Z")

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Thank you, odow. I will report the issue there.