# Optimal with IPOPTH, Infeasible with Gurobi

**URL:** <https://discourse.julialang.org/t/optimal-with-ipopth-infeasible-with-gurobi/48523>\
**Category:** Optimization (Mathematical)\
**Tags:** question, jump\
**Created:** [October 16, 2020, 10:11pm UTC](https://discourse.julialang.org/t/optimal-with-ipopth-infeasible-with-gurobi/48523 "2020-10-16T22:11:18Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![SingingKim](https://avatars.discourse-cdn.com/v4/letter/s/5fc32e/32.png) [@SingingKim](https://discourse.julialang.org/u/SingingKim)\
**Post date:** [October 16, 2020, 10:11pm UTC](https://discourse.julialang.org/t/optimal-with-ipopth-infeasible-with-gurobi/48523/1 "2020-10-16T22:11:18Z")

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Hi, I’m working on a bilevel problem that is converted into an equivalent non-convex QCQP by applying strong duality to the lower-level problem (LP).

My code returns a (local) optimal solution with Ipopt solver (w/ ma86).  
However, the same code returns infeasibility with Gurobi v9.0.2 (NonConvex=2).

This makes me wonder if the solution obtained with Ipopt is reliable.  
Is there any possible reasoning for this? Any advice would be highly appreciated.

Thank you.

```julia
  [a076750e] CPLEX v0.6.5
  [336ed68f] CSV v0.6.2
  [aaaa29a8] Clustering v0.14.1
  [a93c6f00] DataFrames v0.21.3
  [31c24e10] Distributions v0.23.4
  [2e9cd046] Gurobi v0.8.1
  [f67ccb44] HDF5 v0.13.2
  [7073ff75] IJulia v1.21.2
  [b6b21f68] Ipopt v0.6.2
  [4076af6c] JuMP v0.21.3
  [e5e0dc1b] Juno v0.8.2
  [67920dd8] KNITRO v0.9.2
  [23992714] MAT v0.8.0
  [6405355b] Mosek v1.1.3
  [1ec41992] MosekTools v0.9.3
  [8bb1440f] DelimitedFiles

```

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**Author:** ![ccoffrin](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ccoffrin/32/400_2.png) [@ccoffrin](https://discourse.julialang.org/u/ccoffrin)\
**Post date:** [October 16, 2020, 10:48pm UTC](https://discourse.julialang.org/t/optimal-with-ipopth-infeasible-with-gurobi/48523/2 "2020-10-16T22:48:11Z")

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My experience has been that Ipopt is the most numerically stable non-linear solver. In this case, I would suspect there is a numerical issue in Guorbi. One useful diagnostic is to evaluate the feasibility of each constraint in the solution found by Ipopt.

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**Author:** ![SingingKim](https://avatars.discourse-cdn.com/v4/letter/s/5fc32e/32.png) [@SingingKim](https://discourse.julialang.org/u/SingingKim)\
**Post date:** [October 17, 2020, 12:35am UTC](https://discourse.julialang.org/t/optimal-with-ipopth-infeasible-with-gurobi/48523/3 "2020-10-17T00:35:42Z")

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@ccoffrin Thank you for your advice. Is there a smart way to check the feasibility?

The only way I know is to do something like: `value.(g) - value.(d) == 0` for constraint `@constraint(m, const1[t in 1:24], g[t] - d[t] == 0)`  
I just have too many constraints to do this manually.

Also, it is odd to me that Gurobi returns infeasibility rather than taking a longer time, as this means Gurobi fails to find any feasible point if I understand it correctly.

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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:** [October 18, 2020, 8:20pm UTC](https://discourse.julialang.org/t/optimal-with-ipopth-infeasible-with-gurobi/48523/4 "2020-10-18T20:20:46Z")

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> Also, it is odd to me that Gurobi returns infeasibility rather than taking a longer time, as this means Gurobi fails to find any feasible point if I understand it correctly.

I suggest you read [https://www.gurobi.com/documentation/9.0/refman/num\_grb\_guidelines\_for\_num.html](https://www.gurobi.com/documentation/9.0/refman/num_grb_guidelines_for_num.html)

> Is there a smart way to check the feasibility?

Not really. You can use something like the following:

```Julia
model = Model()
@variable(model, x >= 0)
@variable(model, y >= 0)
c = @constraint(model, x * y <= 1)
o = constraint_object(c)
value(o.func) # left-hand side
o.set.upper # right-hand side, if <=. Use .lower if >=, and .value if ==

```

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**Author:** ![SingingKim](https://avatars.discourse-cdn.com/v4/letter/s/5fc32e/32.png) [@SingingKim](https://discourse.julialang.org/u/SingingKim)\
**Post date:** [October 19, 2020, 12:34am UTC](https://discourse.julialang.org/t/optimal-with-ipopth-infeasible-with-gurobi/48523/5 "2020-10-19T00:34:37Z")

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@odow Thank you so much for your comment!