# Gurobi12 reports OPTIMAL to an NLP which is actually UNbounded

**URL:** <https://discourse.julialang.org/t/gurobi12-reports-optimal-to-an-nlp-which-is-actually-unbounded/127293>\
**Category:** Optimization (Mathematical)\
**Tags:** question, jump, gurobi\
**Created:** [March 23, 2025, 11:52pm UTC](https://discourse.julialang.org/t/gurobi12-reports-optimal-to-an-nlp-which-is-actually-unbounded/127293 "2025-03-23T23:52:30Z")\
**Posts on this page:** 10\
**Page:** 1

<div class="post-metadata">

**Author:** ![WalterMadelim](https://avatars.discourse-cdn.com/v4/letter/w/3e96dc/32.png) [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)\
**Post date:** [March 23, 2025, 11:52pm UTC](https://discourse.julialang.org/t/gurobi12-reports-optimal-to-an-nlp-which-is-actually-unbounded/127293/1 "2025-03-23T23:52:30Z")

</div>

Continuing the discussion from [Gurobi12 Reports unbounded to a nonconvex QP which is actually bounded](https://discourse.julialang.org/t/gurobi12-reports-unbounded-to-a-nonconvex-qp-which-is-actually-bounded/126657):

```julia
import JuMP, Gurobi
NLP = JuMP.Model(Gurobi.Optimizer);
JuMP.@variable(NLP, x);
JuMP.@objective(NLP, Min, (x + 1) * x * (x - 1));
JuMP.optimize!(NLP);
Gurobi Optimizer version 12.0.1 build v12.0.1rc0 (win64 - Windows 11.0 (26100.2))

CPU model: 11th Gen Intel(R) Core(TM) i5-1135G7 @ 2.40GHz, instruction set [SSE2|AVX|AVX2|AVX512]
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 0 rows, 3 columns and 0 nonzeros
Model fingerprint: 0x60c267e2
Model has 1 general nonlinear constraint (2 nonlinear terms)
Variable types: 3 continuous, 0 integer (0 binary)
Coefficient statistics:
  Matrix range [0e+00, 0e+00]
  Objective range [1e+00, 1e+00]
  Bounds range [0e+00, 0e+00]
  RHS range [0e+00, 0e+00]
Found heuristic solution: objective 0.0000000
Presolve model has 1 nlconstr
Added 4 variables to disaggregate expressions.
Presolve time: 0.00s
Presolved: 10 rows, 8 columns, 22 nonzeros
Presolved model has 2 bilinear constraint(s)

Solving non-convex MIQCP

Variable types: 8 continuous, 0 integer (0 binary)
Found heuristic solution: objective -0.3849002

Root relaxation: unbounded, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes | Current Node | Objective Bounds | Work
 Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time

     0 0 postponed 0 -0.38490 - - - 0s
omit lines....
* 934 43 124 -210.0000000 - - 0.3 0s
H 8396 1056 -627.4375000 -5.369e+14 - 0.2 0s
omit lines....
 4747770 24 -5.369e+14 39299 1 -2.621e+11 -5.369e+14 - 0.0 120s
 4762410 24 -5.369e+14 39909 1 -2.621e+11 -5.369e+14 - 0.0 125s
H4763874 24 -1.00000e+18 -1.000e+18 0.00% 0.0 125s

Explored 4765338 nodes (186361 simplex iterations) in 125.93 seconds (11.38 work units)
Thread count was 8 (of 8 available processors)

Solution count 10: -1e+18 -3.74409e+09 -3.44774e+09 ... -2.60131e+09
No other solutions better than -1e+18

Optimal solution found (tolerance 1.00e-04)
Best objective -9.999999999990e+17, best bound -9.999999999990e+17, gap 0.0000%

User-callback calls 9533859, time in user-callback 2.53 sec

```

The primal objVal is fine, as it monotonically decreases.  
But it’s weird to see the `ObjBound` firstly goes up and later goes down (the last 2 lines of MIP Logging).  
Furthermore,

```julia
julia> JuMP.termination_status(NLP)
OPTIMAL::TerminationStatusCode = 1

julia> JuMP.primal_status(NLP)
FEASIBLE_POINT::ResultStatusCode = 1

julia> JuMP.objective_value(NLP)
-9.99999999999e17

julia> valueP = Ref{Cdouble}()
Base.RefValue{Float64}(1.202678831762e-311)

julia> err_code = Gurobi.GRBgetdblattr(JuMP.unsafe_backend(NLP), "MaxVio", valueP)
0

julia> valueP[]
0.0

```

It doesn’t terminates with `GRB_INFINITY`.

---

<div class="post-metadata">

**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:** [March 24, 2025, 12:45am UTC](https://discourse.julialang.org/t/gurobi12-reports-optimal-to-an-nlp-which-is-actually-unbounded/127293/2 "2025-03-24T00:45:04Z")

</div>

This is likely a related bug to the previous one you found. I’ll add it to my support ticket.

You should understand the the MINLP solver in Gurobi is new. It is expected that there are a number of bugs, especially with these edge-case models.

---

<div class="post-metadata">

**Author:** ![WalterMadelim](https://avatars.discourse-cdn.com/v4/letter/w/3e96dc/32.png) [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)\
**Post date:** [March 24, 2025, 12:56am UTC](https://discourse.julialang.org/t/gurobi12-reports-optimal-to-an-nlp-which-is-actually-unbounded/127293/3 "2025-03-24T00:56:14Z")

</div>

> [@odow](#):
>
> I’ll add it to my support ticket.

Thank you very much.

Actually here is a nonconvex QCP reformulation of the above NLP, which can be run much faster. This time the upside is: a warning can be seen in Gurobi’s Logging.

The errors are

1. the `best bound` shouldn’t first go up and then go down.
2. the termination status shouldn’t be `OPTIMAL`

Please take a look (Since this is nonconvex QCP, I think Gurobi 9 could do it)

```julia
julia> import JuMP, Gurobi

julia> ncQCP = JuMP.Model(Gurobi.Optimizer) # non-convex QCP
Set parameter Username
Set parameter LicenseID to value 2602363
Academic license - for non-commercial use only - expires 2025-12-20
A JuMP Model
├ solver: Gurobi
├ objective_sense: FEASIBILITY_SENSE
├ num_variables: 0
├ num_constraints: 0
└ Names registered in the model: none

julia> JuMP.@variable(ncQCP, x)
x

julia> JuMP.@variable(ncQCP, xx)
xx

julia> JuMP.@constraint(ncQCP, xx >= x * x)
-x² + xx >= 0

julia> JuMP.@constraint(ncQCP, xx <= x * x)
-x² + xx <= 0

julia> JuMP.@objective(ncQCP, Min, x * (xx - 1))
x*xx - x

julia> JuMP.optimize!(ncQCP)
Gurobi Optimizer version 12.0.1 build v12.0.1rc0 (win64 - Windows 11.0 (26100.2))

CPU model: 11th Gen Intel(R) Core(TM) i5-1135G7 @ 2.40GHz, instruction set [SSE2|AVX|AVX2|AVX512]
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 0 rows, 2 columns and 0 nonzeros
Model fingerprint: 0xb0bb3f9e
Model has 1 quadratic objective term
Model has 2 quadratic constraints
Coefficient statistics:
  Matrix range [0e+00, 0e+00]
  QMatrix range [1e+00, 1e+00]
  QLMatrix range [1e+00, 1e+00]
  Objective range [1e+00, 1e+00]
  QObjective range [2e+00, 2e+00]
  Bounds range [0e+00, 0e+00]
  RHS range [0e+00, 0e+00]

Continuous model is non-convex -- solving as a MIP

Found heuristic solution: objective 0.0000000
Presolve time: 0.00s
Presolved: 3 rows, 4 columns, 6 nonzeros
Presolved model has 1 quadratic constraint(s)
Presolved model has 2 bilinear constraint(s)
Warning: Model contains variables with very large bounds participating
         in product terms.
         Presolve was not able to compute smaller bounds for these variables.
         Consider bounding these variables or reformulating the model.

Variable types: 4 continuous, 0 integer (0 binary)

Root relaxation: unbounded, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes | Current Node | Objective Bounds | Work
 Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time

     0 0 unbounded 0 0.00000 - - - 0s
     0 0 postponed 0 0.00000 - - - 0s
     0 0 postponed 0 0.00000 - - - 0s
     0 0 postponed 0 0.00000 - - - 0s
     0 2 postponed 0 0.00000 - - - 0s
* 1 2 1 -9.99999e+08 - - 4.0 0s
* 4 2 2 -2.82843e+09 - - 2.3 0s
* 7 4 4 -8.00000e+09 - - 2.0 0s
* 21 4 5 -2.26274e+10 - - 1.8 0s
* 23 4 8 -6.40000e+10 - - 1.8 0s
* 45 4 11 -1.81019e+11 - - 1.7 0s
* 99 6 28 -1.81029e+11 - - 1.4 0s
* 119 13 29 -1.81039e+11 - - 1.3 0s
* 140 19 35 -1.81096e+11 - - 1.2 0s
H 158 24 -1.81163e+11 - - 1.1 0s
H 191 42 -1.81288e+11 - - 0.9 0s
* 270 42 69 -1.81423e+11 - - 0.7 0s
* 368 60 71 -1.81442e+11 - - 0.5 0s
* 369 60 72 -1.81452e+11 - - 0.5 0s
* 372 60 73 -1.81461e+11 - - 0.5 0s
* 430 66 74 -1.81471e+11 - - 0.5 0s
* 433 66 75 -1.81481e+11 - - 0.5 0s
* 434 66 76 -1.81490e+11 - - 0.5 0s
* 437 66 77 -1.81500e+11 - - 0.5 0s
* 438 66 78 -1.81509e+11 - - 0.5 0s
* 441 66 79 -1.81519e+11 - - 0.5 0s
* 442 66 80 -1.81529e+11 - - 0.5 0s
* 445 66 81 -1.81538e+11 - - 0.5 0s
* 446 66 82 -1.81548e+11 - - 0.5 0s
H 501 84 -1.81596e+11 - - 0.4 0s
* 527 84 88 -1.81606e+11 - - 0.4 0s
* 530 84 89 -1.81615e+11 - - 0.4 0s
* 531 84 90 -1.81625e+11 - - 0.4 0s
* 534 84 91 -1.81634e+11 - - 0.4 0s
* 535 84 92 -1.81644e+11 - - 0.4 0s
* 538 84 93 -1.81654e+11 - - 0.4 0s
* 539 84 94 -1.81663e+11 - - 0.4 0s
H 602 94 -1.81673e+11 - - 0.4 0s
* 627 94 96 -1.81683e+11 - - 0.4 0s
* 630 94 97 -1.81692e+11 - - 0.4 0s
* 631 94 98 -1.81702e+11 - - 0.4 0s
* 634 94 99 -1.81711e+11 - - 0.4 0s
* 635 94 100 -1.81721e+11 - - 0.4 0s
* 638 94 101 -1.81731e+11 - - 0.4 0s
* 639 94 102 -1.81740e+11 - - 0.4 0s
* 642 94 103 -1.81750e+11 - - 0.4 0s
* 643 94 104 -1.81760e+11 - - 0.4 0s
H 645 94 -1.81769e+11 - - 0.4 0s
* 647 94 106 -1.81779e+11 - - 0.4 0s
* 650 94 107 -1.81788e+11 - - 0.4 0s
* 651 94 108 -1.81798e+11 - - 0.4 0s
* 743 66 109 -1.81808e+11 - - 0.3 0s
* 744 66 110 -1.81817e+11 - - 0.3 0s
* 966 116 151 -1.82212e+11 - - 0.3 0s
* 1563 145 18 -5.12000e+11 -5.369e+14 - 0.2 0s
* 1566 136 19 -1.44815e+12 -5.369e+14 - 0.2 0s
* 1567 129 20 -4.09600e+12 -5.369e+14 - 0.2 0s
* 1569 121 21 -1.15852e+13 -5.369e+14 4534% 0.2 0s
* 1571 115 22 -3.27680e+13 -5.369e+14 1538% 0.2 0s
* 1574 108 24 -2.62144e+14 -5.369e+14 105% 0.2 0s
* 1576 101 25 -7.41455e+14 -7.415e+14 0.00% 0.2 0s

Explored 1579 nodes (341 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 10: -7.41455e+14 -2.62144e+14 -3.2768e+13 ... -1.81808e+11
No other solutions better than -7.41455e+14

Optimal solution found (tolerance 1.00e-04)
Best objective -7.414552000990e+14, best bound -7.414552000990e+14, gap 0.0000%

User-callback calls 3404, time in user-callback 0.00 sec

julia> JuMP.solution_summary(ncQCP; verbose = true)
* Solver : Gurobi

* Status
  Result count : 10
  Termination status : OPTIMAL
  Message from the solver:
  "Model was solved to optimality (subject to tolerances), and an optimal solution is available."

* Candidate solution (result #1)
  Primal status : FEASIBLE_POINT
  Dual status : NO_SOLUTION
  Objective value : -7.41455e+14
  Objective bound : -7.41455e+14
  Relative gap : 0.00000e+00
  Primal solution :
    x : -9.05097e+04
    xx : 8.19200e+09

* Work counters
  Solve time (sec) : 5.99999e-02
  Simplex iterations : 341
  Barrier iterations : 0
  Node count : 1579

```

---

<div class="post-metadata">

**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:** [March 24, 2025, 1:02am UTC](https://discourse.julialang.org/t/gurobi12-reports-optimal-to-an-nlp-which-is-actually-unbounded/127293/4 "2025-03-24T01:02:14Z")

</div>

I’ve submitted a support request with both models.

---

<div class="post-metadata">

**Author:** ![WalterMadelim](https://avatars.discourse-cdn.com/v4/letter/w/3e96dc/32.png) [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)\
**Post date:** [March 25, 2025, 2:34am UTC](https://discourse.julialang.org/t/gurobi12-reports-optimal-to-an-nlp-which-is-actually-unbounded/127293/5 "2025-03-25T02:34:04Z")

</div>

I’m very sorry but I find yet another bug of Gurobi.  
In the following test case I am essentially `Minimize x`, where `x` is free.  
But Gurobi reports `OPTIMAL`

```julia
julia> import JuMP, Gurobi

julia> begin
           model = JuMP.Model(Gurobi.Optimizer)
               JuMP.@variable(model, x)
           JuMP.@variable(model, trivial_decision)
           JuMP.@constraint(model, trivial_decision >= x * x)
           JuMP.@constraint(model, trivial_decision <= x * x)
           JuMP.@objective(model, Min, x)
       end
julia> JuMP.optimize!(model)
Gurobi Optimizer version 12.0.1 build v12.0.1rc0 (win64 - Windows 11.0 (26100.2))

CPU model: 11th Gen Intel(R) Core(TM) i5-1135G7 @ 2.40GHz, instruction set [SSE2|AVX|AVX2|AVX512]
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 0 rows, 2 columns and 0 nonzeros
Model fingerprint: 0x862a5994
Model has 2 quadratic constraints
Coefficient statistics:
  Matrix range [0e+00, 0e+00]
  QMatrix range [1e+00, 1e+00]
  QLMatrix range [1e+00, 1e+00]
  Objective range [1e+00, 1e+00]
  Bounds range [0e+00, 0e+00]
  RHS range [0e+00, 0e+00]

Continuous model is non-convex -- solving as a MIP

Found heuristic solution: objective 0.0000000
Presolve time: 0.00s
Presolved: 1 rows, 3 columns, 2 nonzeros
Presolved model has 1 quadratic constraint(s)
Presolved model has 1 bilinear constraint(s)
Warning: Model contains variables with very large bounds participating
         in product terms.
         Presolve was not able to compute smaller bounds for these variables.
         Consider bounding these variables or reformulating the model.

Variable types: 3 continuous, 0 integer (0 binary)

Root relaxation: unbounded, 0 iterations, 0.00 seconds (0.00 work units)

    Nodes | Current Node | Objective Bounds | Work
 Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time

     0 0 unbounded 0 0.00000 - - - 0s
     0 0 unbounded 0 0.00000 - - - 0s
     0 0 unbounded 0 0.00000 - - - 0s
     0 0 unbounded 0 0.00000 - - - 0s
     0 0 unbounded 0 0.00000 - - - 0s
     0 0 postponed 0 0.00000 - - - 0s
     0 0 postponed 0 0.00000 - - - 0s
     0 2 postponed 0 0.00000 - - - 0s
* 1298 995 14 -1000000.000 - - 0.0 0s
* 1340 933 34 -1024000.000 - - 0.0 0s
* 1347 889 38 -1447680.982 - - 0.0 0s
* 1348 844 38 -1447695.168 - - 0.0 0s
* 1353 800 40 -1448099.336 - - 0.0 0s
* 1366 755 36 -2048000.000 - - 0.0 0s
* 1369 716 38 -2895659.103 - - 0.0 0s
* 1380 669 38 -4096000.000 -4096000.0 0.00% 0.0 0s

Explored 1383 nodes (45 simplex iterations) in 0.66 seconds (0.25 work units)
Thread count was 8 (of 8 available processors)

Solution count 9: -4.096e+06 -2.89566e+06 -2.048e+06 ... 0
No other solutions better than -4.096e+06

Optimal solution found (tolerance 1.00e-04)
Best objective -4.096000000000e+06, best bound -4.096000000000e+06, gap 0.0000%

User-callback calls 2908, time in user-callback 0.00 sec

julia> JuMP.solution_summary(model; verbose = true)
* Solver : Gurobi

* Status
  Result count : 9
  Termination status : OPTIMAL
  Message from the solver:
  "Model was solved to optimality (subject to tolerances), and an optimal solution is available."

* Candidate solution (result #1)
  Primal status : FEASIBLE_POINT
  Dual status : NO_SOLUTION
  Objective value : -4.09600e+06
  Objective bound : -4.09600e+06
  Relative gap : 0.00000e+00
  Primal solution :
    trivial_decision : 1.67772e+13
    x : -4.09600e+06

* Work counters
  Solve time (sec) : 6.59000e-01
  Simplex iterations : 45
  Barrier iterations : 146215
  Node count : 1383

```

But we may learn from this case that if Gurobi prints `Warning`, then it may be a sign of potential misfortune. Therefore we have to also strive to eliminate solver’s Warnings to ensure normality, and the expected behavior.

---

<div class="post-metadata">

**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:** [March 25, 2025, 3:33am UTC](https://discourse.julialang.org/t/gurobi12-reports-optimal-to-an-nlp-which-is-actually-unbounded/127293/6 "2025-03-25T03:33:52Z")

</div>

I’ll add it to the list. I assume that these are all in fact different models that hit the same bug, rather than different bugs entirely.

---

<div class="post-metadata">

**Author:** ![WalterMadelim](https://avatars.discourse-cdn.com/v4/letter/w/3e96dc/32.png) [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)\
**Post date:** [April 6, 2025, 6:18am UTC](https://discourse.julialang.org/t/gurobi12-reports-optimal-to-an-nlp-which-is-actually-unbounded/127293/7 "2025-04-06T06:18:00Z")

</div>

This behavior was under the default setting or Presolve = 1,  
if we `set_attribute(model, "Presolve", 2)`, then it becomes correct though (see the last line).

```julia
Non-default parameters:
Presolve 2

Optimize a model with 0 rows, 2 columns and 0 nonzeros
Model fingerprint: 0x862a5994
Model has 2 quadratic constraints
Coefficient statistics: # omit this

Continuous model is non-convex -- solving as a MIP

Found heuristic solution: objective 0.0000000
Presolve time: 0.00s
Presolved: 1 rows, 3 columns, 2 nonzeros
Presolved model has 1 quadratic constraint(s)
Presolved model has 1 bilinear constraint(s)
Warning: Model contains variables with very large bounds participating
         in product terms.
         Presolve was not able to compute smaller bounds for these variables.
         Consider bounding these variables or reformulating the model.

Variable types: 3 continuous, 0 integer (0 binary)

Root relaxation: unbounded, 0 iterations, 0.00 seconds (0.00 work units)

    Nodes | Current Node | Objective Bounds | Work
 Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time

     0 0 unbounded 0 0.00000 - - - 0s

Explored 1 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 1: 0

Model is unbounded # ✅ This conclusion is correct

```

---

<div class="post-metadata">

**Author:** ![WalterMadelim](https://avatars.discourse-cdn.com/v4/letter/w/3e96dc/32.png) [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)\
**Post date:** [April 6, 2025, 6:21am UTC](https://discourse.julialang.org/t/gurobi12-reports-optimal-to-an-nlp-which-is-actually-unbounded/127293/8 "2025-04-06T06:21:29Z")

</div>

If Presolve = 0, it will continually executing MIP logging for a (maybe nondeterministic) long time

```julia
    Nodes | Current Node | Objective Bounds | Work
 Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time

     0 0 unbounded 0 0.00000 - - - 0s
# omit lines
 1085537 5391 postponed 48 0.00000 - - 0.0 715s
 1091863 5378 postponed 50 0.00000 - - 0.0 720s
# omit lines

```

---

<div class="post-metadata">

**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:** [April 6, 2025, 8:03am UTC](https://discourse.julialang.org/t/gurobi12-reports-optimal-to-an-nlp-which-is-actually-unbounded/127293/9 "2025-04-06T08:03:40Z")

</div>

There is little point trying to understand the behavior of Gurobi on this model with different parameter settings because there is a bug.

---

<div class="post-metadata">

**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:** [May 14, 2025, 1:07am UTC](https://discourse.julialang.org/t/gurobi12-reports-optimal-to-an-nlp-which-is-actually-unbounded/127293/10 "2025-05-14T01:07:05Z")

</div>

Gurobi\_jll@12.0.2 now returns

```Julia
julia> using JuMP, Gurobi

julia> begin
           model = Model(Gurobi.Optimizer)
           @variable(model, x)
           @objective(model, Min, (x + 1) * x * (x - 1))
           optimize!(model)
           solution_summary(model)
       end
solution_summary(; result = 1, verbose = false)
├ solver_name : Gurobi
├ Termination
│ ├ termination_status : LOCALLY_SOLVED
│ ├ result_count : 10
│ ├ raw_status : Unable to satisfy optimality tolerances; a sub-optimal solution is available.
│ └ objective_bound : -1.00000e+100
├ Solution (result = 1)
│ ├ primal_status : FEASIBLE_POINT
│ ├ dual_status : NO_SOLUTION
│ ├ objective_value : -8.19232e+09
│ ├ dual_objective_value : 0.00000e+00
│ └ relative_gap : 1.00000e+100
└ Work counters
  ├ solve_time (sec) : 3.11175e+01
  ├ simplex_iterations : 43894
  ├ barrier_iterations : 0
  └ node_count : 309152

```