maximization problem

[joseph-gergaud]

We want to use ADNPLModel and Ipopt for a maximization problem and not for a minimization one. Of course, We can we can give to ADNLProblem the opposite of the objective function. But is it possible :

• to say to the model that it's a maximization problem ?
• to give to the function ipopt from NLPModelsIpopt.jl that it's a maximization problem ?
  Thanks

[tmigot]

Hi @joseph-gergaud ,

It is possible.

• The NLPModels have a boolean attribute minimize in their meta, so doing nlp.meta.minimize will say whether or not it is a minimization problem. Please take a look at the example below.
• NLPModelsIpopt will accept the maximization problem, but note that it just multiplies by -1 the objective and then call IPOPT on the minimization problem, see https://github.com/JuliaSmoothOptimizers/NLPModelsIpopt.jl/blob/6ede855e6ad2cef94590900302919818141e7f57/src/NLPModelsIpopt.jl#L219

Note, however, that (for now at least) not all the JuliaSmoothOptimizers solvers accept maximization formulation.

The following is possible:

julia> using ADNLPModels
julia> nlp = ADNLPModel(x -> sum(x), ones(2), minimize = false)
ADNLPModel - Model with automatic differentiation backend ADModelBackend{
  ForwardDiffADGradient,
  ForwardDiffADHvprod,
  ForwardDiffADJprod,
  ForwardDiffADJtprod,
  SparseADJacobian,
  ForwardDiffADHessian,
  ForwardDiffADGHjvprod,
}
  Problem name: Generic
   All variables: ████████████████████ 2      All constraints: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
            free: ████████████████████ 2                 free: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
           lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
           upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
         low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0              low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
           fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
          infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
            nnzh: (  0.00% sparsity)   3               linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
                                                    nonlinear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
                                                         nnzj: (------% sparsity)

  Counters:
             obj: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 grad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 cons: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
        cons_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0             cons_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 jcon: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
           jgrad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                  jac: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0              jac_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
         jac_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                jprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0            jprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
       jprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               jtprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0           jtprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
      jtprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 hess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                hprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
           jhess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               jhprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0

you can check that it worked

julia> nlp.meta.minimize
false

and IPOPT will understand it

julia> stats = ipopt(nlp)

******************************************************************************
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 5.5.1.

Number of nonzeros in equality constraint Jacobian...:        0
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:        3

Total number of variables............................:        2
                     variables with only lower bounds:        0
                variables with lower and upper bounds:        0
                     variables with only upper bounds:        0
Total number of equality constraints.................:        0
Total number of inequality constraints...............:        0
        inequality constraints with only lower bounds:        0
   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  2.0000000e+00 0.00e+00 1.00e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1  2.0002000e+04 0.00e+00 1.00e+00  -1.7 1.00e+04  -4.0 1.00e+00 1.00e+00f  1
   2  8.0002000e+04 0.00e+00 1.00e+00  -1.7 3.00e+04  -4.5 1.00e+00 1.00e+00f  1
   3  2.6000200e+05 0.00e+00 1.00e+00  -1.7 9.00e+04  -5.0 1.00e+00 1.00e+00f  1
   4  8.0000200e+05 0.00e+00 1.00e+00  -1.7 2.70e+05  -5.4 1.00e+00 1.00e+00f  1
   5  2.4200020e+06 0.00e+00 1.00e+00  -1.7 8.10e+05  -5.9 1.00e+00 1.00e+00f  1
   6  7.2800020e+06 0.00e+00 1.00e+00  -1.7 2.43e+06  -6.4 1.00e+00 1.00e+00f  1
   7  2.1860002e+07 0.00e+00 1.00e+00  -1.7 7.29e+06  -6.9 1.00e+00 1.00e+00f  1
   8  6.5600002e+07 0.00e+00 1.00e+00  -1.7 2.19e+07  -7.3 1.00e+00 1.00e+00f  1
   9  1.9682000e+08 0.00e+00 1.00e+00  -1.7 6.56e+07  -7.8 1.00e+00 1.00e+00f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  10  5.9048000e+08 0.00e+00 1.00e+00  -1.7 1.97e+08  -8.3 1.00e+00 1.00e+00f  1
  11  1.7714600e+09 0.00e+00 1.00e+00  -1.7 5.90e+08  -8.8 1.00e+00 1.00e+00f  1
  12  5.3144000e+09 0.00e+00 1.00e+00  -1.7 1.77e+09  -9.2 1.00e+00 1.00e+00f  1
  13  1.5943220e+10 0.00e+00 1.00e+00  -1.7 5.31e+09  -9.7 1.00e+00 1.00e+00f  1
  14  4.7829680e+10 0.00e+00 1.00e+00  -1.7 1.59e+10 -10.2 1.00e+00 1.00e+00f  1
  15  1.4348906e+11 0.00e+00 1.00e+00  -1.7 4.78e+10 -10.7 1.00e+00 1.00e+00f  1
  16  4.3046720e+11 0.00e+00 1.00e+00  -1.7 1.43e+11 -11.2 1.00e+00 1.00e+00f  1
  17  1.2914016e+12 0.00e+00 1.00e+00  -1.7 4.30e+11 -11.6 1.00e+00 1.00e+00f  1
  18  3.8742049e+12 0.00e+00 1.00e+00  -1.7 1.29e+12 -12.1 1.00e+00 1.00e+00f  1
  19  1.1622615e+13 0.00e+00 1.00e+00  -1.7 3.87e+12 -12.6 1.00e+00 1.00e+00f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  20  3.4867844e+13 0.00e+00 1.00e+00  -1.7 1.16e+13 -13.1 1.00e+00 1.00e+00f  1
  21  1.0460353e+14 0.00e+00 1.00e+00  -1.7 3.49e+13 -13.5 1.00e+00 1.00e+00f  1
  22  3.1381060e+14 0.00e+00 1.00e+00  -1.7 1.05e+14 -14.0 1.00e+00 1.00e+00f  1
  23  9.4143179e+14 0.00e+00 1.00e+00  -1.7 3.14e+14 -14.5 1.00e+00 1.00e+00f  1
  24  2.8242954e+15 0.00e+00 1.00e+00  -1.7 9.41e+14 -15.0 1.00e+00 1.00e+00f  1
  25  8.4728861e+15 0.00e+00 1.00e+00  -1.7 2.82e+15 -15.5 1.00e+00 1.00e+00f  1
  26  2.5418658e+16 0.00e+00 1.00e+00  -1.7 8.47e+15 -15.9 1.00e+00 1.00e+00f  1
  27  7.6255975e+16 0.00e+00 1.00e+00  -1.7 2.54e+16 -16.4 1.00e+00 1.00e+00f  1
  28  2.2876792e+17 0.00e+00 1.00e+00  -1.7 7.63e+16 -16.9 1.00e+00 1.00e+00f  1
  29  6.8630377e+17 0.00e+00 1.00e+00  -1.7 2.29e+17 -17.4 1.00e+00 1.00e+00f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  30  2.0589113e+18 0.00e+00 1.00e+00  -1.7 6.86e+17 -17.8 1.00e+00 1.00e+00f  1
  31  6.1767340e+18 0.00e+00 1.00e+00  -1.7 2.06e+18 -18.3 1.00e+00 1.00e+00f  1
  32  1.8530202e+19 0.00e+00 1.00e+00  -1.7 6.18e+18 -18.8 1.00e+00 1.00e+00f  1
  33  5.5590606e+19 0.00e+00 1.00e+00  -1.7 1.85e+19 -19.3 1.00e+00 1.00e+00f  1
  34  1.6677182e+20 0.00e+00 1.00e+00  -1.7 5.56e+19 -19.7 1.00e+00 1.00e+00f  1
  35  3.6677182e+20 0.00e+00 1.00e+00  -1.7 1.00e+20 -20.0 1.00e+00 1.00e+00f  1

Number of Iterations....: 35

                                   (scaled)                 (unscaled)
Objective...............:  -3.6677181699666595e+20    3.6677181699666595e+20
Dual infeasibility......:   1.0000000000000000e+00    1.0000000000000000e+00
Constraint violation....:   0.0000000000000000e+00    0.0000000000000000e+00
Variable bound violation:   0.0000000000000000e+00    0.0000000000000000e+00
Complementarity.........:   0.0000000000000000e+00    0.0000000000000000e+00
Overall NLP error.......:   1.0000000000000000e+00    1.0000000000000000e+00


Number of objective function evaluations             = 36
Number of objective gradient evaluations             = 36
Number of equality constraint evaluations            = 0
Number of inequality constraint evaluations          = 0
Number of equality constraint Jacobian evaluations   = 0
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations             = 35
Total seconds in IPOPT                               = 10.123

EXIT: Iterates diverging; problem might be unbounded.
"Execution stats: unknown"

julia> stats.solution
2-element Vector{Float64}:
 1.8338590849833298e20
 1.8338590849833298e20

[joseph-gergaud]

Thanks,