[FileFormats.MOF] Fix reading of NLPs

[odow]

Closes #1906

julia> using JuMP, Ipopt

julia> model = read_from_file("test/FileFormats/MOF/nlp.mof.json")
A JuMP Model
Minimization problem with:
Variables: 4
Objective function type: AffExpr
`VariableRef`-in-`MathOptInterface.Interval{Float64}`: 4 constraints
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.

julia> set_optimizer(model, Ipopt.Optimizer)

julia> optimize!(model)

******************************************************************************
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
******************************************************************************

This is Ipopt version 3.14.4, running with linear solver MUMPS 5.4.1.

Number of nonzeros in equality constraint Jacobian...:        4
Number of nonzeros in inequality constraint Jacobian.:        4
Number of nonzeros in Lagrangian Hessian.............:       24

Total number of variables............................:        4
                     variables with only lower bounds:        0
                variables with lower and upper bounds:        4
                     variables with only upper bounds:        0
Total number of equality constraints.................:        1
Total number of inequality constraints...............:        1
        inequality constraints with only lower bounds:        1
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
   0  4.1009029e+00 3.59e+01 1.54e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1  6.3052937e+00 3.43e+01 2.33e+01  -1.0 5.89e+00    -  2.21e-03 4.20e-02h  1
   2  5.3929003e+00 3.42e+01 7.45e+02  -1.0 3.89e+00   2.0 6.10e-06 3.54e-03F  1
   3  6.6372159e+01 6.01e+00 2.27e+05  -1.0 3.78e+00   4.2 9.48e-04 4.80e-01h  2
   4  9.6419121e+01 4.30e-01 5.82e+04  -1.0 7.23e+01    -  1.59e-02 1.00e+00h  1
   5  9.4884972e+01 1.15e-03 3.12e+02  -1.0 1.47e+00    -  1.00e+00 1.00e+00h  1
   6  8.7460064e+01 8.24e-02 1.95e+01  -1.0 6.98e-01    -  1.00e+00 1.00e+00f  1
   7  8.9880566e+01 9.69e-03 3.14e+02  -1.0 7.37e-02   3.8 1.00e+00 1.00e+00h  1
   8  8.9330308e+01 3.71e-04 1.71e+01  -1.0 2.19e-01    -  1.00e+00 1.00e+00f  1
   9  8.9331900e+01 1.73e-06 4.10e+00  -1.0 2.16e-03   3.3 1.00e+00 1.00e+00h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  10  8.0133699e+01 1.20e-01 1.86e+01  -1.0 2.30e+00    -  1.00e+00 1.00e+00f  1
  11  8.2219265e+01 7.59e-03 3.27e+01  -1.0 6.41e-02   2.8 1.00e+00 1.00e+00h  1
  12  7.5619844e+01 5.78e-02 1.78e+01  -1.0 2.89e+00    -  1.00e+00 1.00e+00f  1
  13  7.6383207e+01 1.10e-03 4.23e+00  -1.0 2.53e-02   2.3 1.00e+00 1.00e+00h  1
  14  5.6773756e+01 5.44e-01 1.90e+01  -1.0 1.15e+01    -  1.00e+00 1.00e+00f  1
  15  6.0190720e+01 2.74e-02 5.29e+00  -1.0 1.24e-01   1.8 1.00e+00 1.00e+00h  1
  16  2.8936531e+01 1.69e+00 2.27e+01  -1.0 3.26e+01    -  1.00e+00 1.00e+00f  1
  17  3.1904315e+01 6.64e-02 1.11e+00  -1.0 1.93e-01   1.4 1.00e+00 1.00e+00h  1
  18  2.0735088e+01 3.84e-01 1.76e+00  -1.0 9.22e+01    -  1.00e+00 1.99e-01f  1
  19  1.7114152e+01 5.20e-01 8.02e+00  -1.0 4.71e+01    -  1.00e+00 1.30e-01f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  20  1.7278457e+01 3.55e-02 1.54e-02  -1.0 4.07e-01    -  1.00e+00 1.00e+00h  1
  21  1.7045230e+01 8.77e-03 6.88e-03  -1.7 4.41e-01    -  1.00e+00 1.00e+00h  1
  22  1.7017006e+01 2.40e-03 2.52e-03  -2.5 3.47e-02    -  1.00e+00 1.00e+00h  1
  23  1.7014119e+01 1.90e-04 1.03e-04  -3.8 6.30e-03    -  1.00e+00 1.00e+00h  1
  24  1.7014020e+01 2.57e-07 3.19e-07  -5.7 3.46e-04    -  1.00e+00 1.00e+00h  1
  25  1.7014017e+01 1.96e-11 2.80e-11  -8.6 3.31e-06    -  1.00e+00 1.00e+00h  1

Number of Iterations....: 25

                                   (scaled)                 (unscaled)
Objective...............:   1.7014017145174137e+01    1.7014017145174137e+01
Dual infeasibility......:   2.7982229154407120e-11    2.7982229154407120e-11
Constraint violation....:   1.9625190361693967e-11    1.9625190361693967e-11
Variable bound violation:   7.6745495514174422e-09    7.6745495514174422e-09
Complementarity.........:   2.5297906848701602e-09    2.5297906848701602e-09
Overall NLP error.......:   2.5297906848701602e-09    2.5297906848701602e-09


Number of objective function evaluations             = 30
Number of objective gradient evaluations             = 26
Number of equality constraint evaluations            = 30
Number of inequality constraint evaluations          = 30
Number of equality constraint Jacobian evaluations   = 26
Number of inequality constraint Jacobian evaluations = 26
Number of Lagrangian Hessian evaluations             = 25
Total seconds in IPOPT                               = 2.357

EXIT: Optimal Solution Found.

julia> value.(all_variables(model))
4-element Vector{Float64}:
 0.9999999923254504
 4.742999641809567
 3.8211499817890435
 1.3794082897520368

julia> print(backend(model))

Minimize Nonlinear:
 var_1 * var_4 * (var_1 + var_2 + var_3) + var_3

Subject to:

VariableIndex-in-Interval{Float64}
 var_1 ∈ [1.0, 5.0]
 var_2 ∈ [1.0, 5.0]
 var_3 ∈ [1.0, 5.0]
 var_4 ∈ [1.0, 5.0]

Nonlinear
 var_1 * var_2 * var_3 * var_4 >= 25.0
 var_1 ^ 2.0 + var_2 ^ 2.0 + var_3 ^ 2.0 + var_4 ^ 2.0 == 40.0

[odow]

cc @pulsipher here you go. This is probably only suitable for small to medium sized problems. Parsing the nonlinear JSON allocates quite a lot, so it won't be as efficient as .nl files.

[pulsipher]

Thanks for the fast turn around, I'll forward this on to the Pyomo folks.

[odow]

I'll forward this on to the Pyomo folks.

I'd say it's still somewhat experimental performance-wise. I don't think we've had any serious stress-tests of it, so it'd be good to hear feedback.