[FileFormats.MPS] fix scale factor in Gurobi's QCMATRIX

[odow]

Closes #2627

I still need better testing for this.

The underlying issue is that Gurobi's QCMATRIX section does not match CPLEX and Mosek (It is missing a /2): https://docs.gurobi.com/projects/optimizer/en/current/reference/fileformats/modelformats.html#qcmatrix-section

[odow]

Now I get the correct solution:

julia> using JuMP, Gurobi

julia> filename = "/Users/oscar/Downloads/Initial_problem_set/Test_prob_20.mps"
"/Users/oscar/Downloads/Initial_problem_set/Test_prob_20.mps"

julia> model = read_from_file(filename)
obj
├ solver: none
├ objective_sense: MIN_SENSE
│ └ objective_function_type: AffExpr
├ num_variables: 2518
├ num_constraints: 4346
│ ├ AffExpr in MOI.EqualTo{Float64}: 391
│ ├ AffExpr in MOI.LessThan{Float64}: 400
│ ├ QuadExpr in MOI.EqualTo{Float64}: 1284
│ ├ VariableRef in MOI.GreaterThan{Float64}: 1793
│ ├ VariableRef in MOI.LessThan{Float64}: 78
│ └ VariableRef in MOI.ZeroOne: 400
└ Names registered in the model: none

julia> set_optimizer(model, Gurobi.Optimizer)
Set parameter LicenseID to value 890341

julia> optimize!(model)
Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[x86] - Darwin 24.1.0 24B83)

CPU model: Intel(R) Core(TM) i5-8259U CPU @ 2.30GHz
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 791 rows, 2518 columns and 5384 nonzeros
Model fingerprint: 0xbc4cd974
Model has 1284 quadratic constraints
Variable types: 2118 continuous, 400 integer (400 binary)
Coefficient statistics:
  Matrix range     [4e-03, 2e+02]
  QMatrix range    [1e+00, 1e+00]
  QLMatrix range   [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [8e+00, 1e+05]
  RHS range        [3e+00, 3e+04]
Presolve removed 263 rows and 1315 columns
Presolve time: 0.01s
Presolved: 1784 rows, 1204 columns, 4909 nonzeros
Presolved model has 314 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.


Solving non-convex MIQCP

Variable types: 798 continuous, 406 integer (406 binary)
Found heuristic solution: objective 1192.2587333

Root relaxation: objective 2.832780e+02, 826 iterations, 0.01 seconds (0.01 work units)

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

     0     0  283.27800    0   55 1192.25873  283.27800  76.2%     -    0s
H    0     0                     700.4259893  283.27800  59.6%     -    0s
H    0     0                     695.3995543  283.27800  59.3%     -    0s
H    0     0                     690.4524243  283.27800  59.0%     -    0s
     0     0  296.30035    0   56  690.45242  296.30035  57.1%     -    0s
H    0     0                     689.1690910  296.40604  57.0%     -    0s
H    0     0                     686.4094214  296.40604  56.8%     -    0s
     0     0  296.46363    0   55  686.40942  296.46363  56.8%     -    0s
     0     0  296.93701    0   44  686.40942  296.93701  56.7%     -    0s
H    0     0                     683.3435487  296.93701  56.5%     -    0s
     0     0  296.93701    0   44  683.34355  296.93701  56.5%     -    0s
     0     0  329.80643    0  162  683.34355  329.80643  51.7%     -    0s
H    0     0                     674.1846106  332.82229  50.6%     -    0s
H    0     0                     669.2743489  332.82229  50.3%     -    0s
H    0     0                     668.4192038  332.82229  50.2%     -    0s
     0     2  332.82229    0  162  668.41920  332.82229  50.2%     -    0s
H  272   297                     654.4575487  379.87319  42.0%   135    0s
H  441   454                     626.2078539  379.87319  39.3%   112    1s
H  675   577                     622.2688539  414.17694  33.4%  92.2    1s
H  678   603                     612.2159838  414.17694  32.3%  92.7    1s
H 1166   941                     610.4720390  589.66608  3.41%  92.9    2s
H 1166   894                     609.4456039  589.66608  3.25%  92.9    2s
H 1167   849                     599.1760747  594.50476  0.78%  92.8    2s
H 1171   810                     598.9191764  594.70995  0.70%  93.2    2s

Cutting planes:
  Gomory: 1
  Cover: 4
  MIR: 9
  Flow cover: 9

Explored 1255 nodes (112627 simplex iterations) in 3.10 seconds (2.25 work units)
Thread count was 8 (of 8 available processors)

Solution count 10: 598.919 599.176 609.446 ... 669.274

Optimal solution found (tolerance 1.00e-04)
Best objective 5.989191764127e+02, best bound 5.989191764127e+02, gap 0.0000%

User-callback calls 4360, time in user-callback 0.01 sec

where previously I got

julia> optimize!(model)
Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[x86] - Darwin 24.1.0 24B83)

CPU model: Intel(R) Core(TM) i5-8259U CPU @ 2.30GHz
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 791 rows, 2518 columns and 5384 nonzeros
Model fingerprint: 0xc497b58d
Model has 1284 quadratic constraints
Variable types: 2118 continuous, 400 integer (400 binary)
Coefficient statistics:
  Matrix range     [4e-03, 2e+02]
  QMatrix range    [5e-01, 5e-01]
  QLMatrix range   [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [8e+00, 1e+05]
  RHS range        [3e+00, 3e+04]
Presolve removed 263 rows and 326 columns
Presolve time: 0.00s

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

Solution count 0

Model is infeasible or unbounded
Best objective -, best bound -, gap -

User-callback calls 126, time in user-callback 0.00 sec