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EAGO times out out trivial problem #141

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@odow

Description

See this example:

julia> using JuMP, EAGO

julia> model = Model(EAGO.Optimizer)
A JuMP Model
├ solver: EAGO - Easy Advanced Global Optimization
├ objective_sense: FEASIBILITY_SENSE
├ num_variables: 0
├ num_constraints: 0
└ Names registered in the model: none

julia> @variable(model, x <= 2)
x

julia> @variable(model, t)
t

julia> @constraint(model, log(x) >= t)
log(x) - t  0

julia> @objective(model, Max, t)
t

julia> optimize!(model)
┌ Warning: At least one branching variable is unbounded. This will interfere with EAGO's global
│ optimization routine and may cause unexpected results. Bounds have been automatically
│ generated at +/- 1E10 for all unbounded variables, but tighter user-defined bounds are
│ highly recommended. To disable this warning and the automatic generation of bounds, use
│ the option `unbounded_check = false`.
└ @ EAGO ~/.julia/packages/EAGO/oWEmA/src/eago_optimizer/optimize/nonconvex/stack_management.jl:256

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
 Ipopt is released as open source code under the Eclipse Public License (EPL).
         For more information visit https://github.com/coin-or/Ipopt
******************************************************************************

---------------------------------------------------------------------------------------------------------------------------------
|  Iteration #  |     Nodes     |  Lower Bound  |  Upper Bound  |      Gap      |     Ratio     |     Timer     |   Time Left   |
---------------------------------------------------------------------------------------------------------------------------------
|          1000 |            21 |    -1.000E+10 |           Inf |           Inf |           Inf |         10.98 |       3589.02 |
|          2000 |            21 |    -1.000E+10 |           Inf |           Inf |           Inf |         12.30 |       3587.70 |
|          3000 |            19 |    -1.000E+10 |           Inf |           Inf |           Inf |         13.57 |       3586.43 |
|          4000 |            21 |    -1.000E+10 |           Inf |           Inf |           Inf |         14.90 |       3585.10 |
|          5000 |            19 |    -1.000E+10 |           Inf |           Inf |           Inf |         16.21 |       3583.79 |
|          6000 |            21 |    -1.000E+10 |           Inf |           Inf |           Inf |         17.53 |       3582.47 |
|          7000 |            19 |    -1.000E+10 |           Inf |           Inf |           Inf |         18.81 |       3581.19 |
|          8000 |            21 |    -1.000E+10 |           Inf |           Inf |           Inf |         20.11 |       3579.89 |
|          9000 |            17 |    -1.000E+10 |           Inf |           Inf |           Inf |         21.41 |       3578.59 |
|         10000 |            19 |    -1.000E+10 |           Inf |           Inf |           Inf |         22.72 |       3577.28 |
|         11000 |            19 |    -1.000E+10 |           Inf |           Inf |           Inf |         24.03 |       3575.97 |
|         12000 |            19 |    -1.000E+10 |           Inf |           Inf |           Inf |         25.36 |       3574.64 |
|         13000 |            19 |    -1.000E+10 |           Inf |           Inf |           Inf |         26.67 |       3573.33 |
|         14000 |            17 |    -1.000E+10 |           Inf |           Inf |           Inf |         28.00 |       3572.00 |
|         15000 |            17 |    -1.000E+10 |           Inf |           Inf |           Inf |         29.28 |       3570.72 |

I expected it to solve quickly.

Found because I've been adding new tests to MOI. I'll fix the test in MOI to add finite bounds, but I thought this was an interesting test case.

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