Consumption housing model, imprecise solution

[azev77]

using InfiniteOpt, Ipopt
ρ = 0.025  # discount rate
T = 10.0   # life horizon
r = 0.05   # interest rate
B0 = 100.0 # endowment
δ = 0.10
u(c, H) = log(c) + log(H)
discount(t; ρ=ρ) = exp(-ρ*t) # discount function
BC1(B, c, iH, H; r=r) = r*B - c -iH     # budget constraint
BC2(B, c, iH, H; δ=δ) = iH - δ*H     # budget constraint
opt = Ipopt.Optimizer   # desired solver
ns = 10_000;             # number of points in the time grid

m = InfiniteModel(opt)
@infinite_parameter(m, t in [0, T], num_supports = ns)
@variable(m, B, Infinite(t)) ## state variables
@variable(m, H, Infinite(t), start = 1) ## state variables
@variable(m, c, Infinite(t), start = 1) ## control variables. Initial guess c(t)=1. Ipopt default initial guess c(t)=1.
@variable(m, iH, Infinite(t))
@objective(m, Max, integral(u(c,H), t, weight_func = discount))
@constraint(m, B(0) == B0)
@constraint(m, B(T) == 0)
@constraint(m, c1, deriv(B, t) == BC1(B, c, iH, H; r=r))
@constraint(m, c2, deriv(H, t) == BC2(B, c, iH, H; δ=δ))
optimize!(m)

I get

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

Number of nonzeros in equality constraint Jacobian...:   129996
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:    20000

Total number of variables............................:    60000
                     variables with only lower bounds:        0
                variables with lower and upper bounds:        0
                     variables with only upper bounds:        0
Total number of equality constraints.................:    40000
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  0.0000000e+00 1.00e+02 1.58e-03  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
   1  1.0211129e+00 9.84e+01 2.05e-03  -1.0 1.00e+02  -4.0 1.00e+00 1.56e-02h  7
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
   2  2.1269107e+00 9.69e+01 4.81e-03  -1.0 1.38e+02  -4.5 1.00e+00 1.56e-02h  7
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
   3  3.2644738e+00 9.54e+01 2.71e-02  -1.0 2.43e+02  -5.0 1.00e+00 1.56e-02h  7
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
   4  4.2974024e+00 9.39e+01 1.19e+00  -1.0 3.38e+02  -5.4 1.00e+00 1.56e-02h  7
Warning: Cutting back alpha due to evaluation error
   5  1.9879886e+01 4.69e+01 3.43e+00  -1.0 3.66e+02  -5.9 1.00e+00 5.00e-01h  2
   6  3.1857875e+01 2.84e-14 2.47e+00  -1.0 4.69e+01  -6.4 1.00e+00 1.00e+00h  1
   7  3.9046104e+01 2.49e-14 1.31e+00  -1.0 1.07e+02  -6.9 1.00e+00 1.00e+00f  1
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
   8  4.0844892e+01 2.84e-14 1.05e+00  -1.0 4.08e+02  -7.3 1.00e+00 2.50e-01f  3
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
   9  4.1276286e+01 2.93e-14 9.91e-01  -1.0 1.13e+03  -7.8 1.00e+00 6.25e-02f  5
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
Warning: Cutting back alpha due to evaluation error
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  10  4.1690858e+01 3.46e-14 9.33e-01  -1.7 1.19e+03  -8.3 1.00e+00 6.25e-02f  5
Warning: Cutting back alpha due to evaluation error
  11  4.4332627e+01 2.84e-14 6.38e-01  -1.7 2.07e+02  -8.8 1.00e+00 5.00e-01f  2
  12  4.7819337e+01 1.14e-13 3.64e-01  -1.7 2.76e+02  -9.2 1.00e+00 1.00e+00f  1
  13  4.9273785e+01 1.14e-13 2.44e-01  -1.7 5.24e+02  -9.7 1.00e+00 1.00e+00f  1
  14  4.9478181e+01 4.55e-13 1.97e-01  -1.7 9.76e+02 -10.2 1.00e+00 1.00e+00f  1
  15  4.9556585e+01 2.27e-13 1.78e-01  -2.5 1.77e+03 -10.7 1.00e+00 1.00e+00f  1
  16  5.1748170e+01 1.82e-12 1.53e-01  -2.5 1.00e+04 -11.2 1.00e+00 1.00e+00f  1
  17  6.3963326e+01 1.46e-11 4.68e-02  -2.5 9.16e+04 -11.6 1.00e+00 1.00e+00f  1
  18  7.6200786e+01 1.82e-12 2.36e-02  -2.5 1.13e+05 -12.1 1.00e+00 1.00e+00f  1
  19  8.8447002e+01 2.91e-11 1.18e-02  -3.8 1.23e+05 -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  1.0069746e+02 5.82e-11 5.92e-03  -3.8 1.50e+05 -13.1 1.00e+00 1.00e+00f  1
  21  1.1295027e+02 5.82e-11 2.97e-03  -3.8 1.97e+05 -13.5 1.00e+00 1.00e+00f  1
  22  1.2520440e+02 1.16e-10 1.48e-03  -3.8 2.73e+05 -14.0 1.00e+00 1.00e+00f  1
  23  1.3745919e+02 2.33e-10 7.42e-04  -5.7 3.92e+05 -14.5 1.00e+00 1.00e+00f  1
  24  1.4971418e+02 2.33e-10 3.71e-04  -5.7 5.80e+05 -15.0 1.00e+00 1.00e+00f  1
  25  1.6196900e+02 4.66e-10 1.86e-04  -5.7 8.79e+05 -15.5 1.00e+00 1.00e+00f  1
  26  1.7422330e+02 4.66e-10 9.29e-05  -5.7 1.38e+06 -15.9 1.00e+00 1.00e+00f  1
  27  1.8647676e+02 9.31e-10 4.65e-05  -5.7 2.47e+06 -16.4 1.00e+00 1.00e+00f  1
  28  1.9872903e+02 1.86e-09 2.32e-05  -5.7 4.41e+06 -16.9 1.00e+00 1.00e+00f  1
  29  2.1097976e+02 3.73e-09 1.16e-05  -5.7 7.87e+06 -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  2.2322852e+02 3.73e-09 5.81e-06  -8.6 1.40e+07 -17.8 1.00e+00 1.00e+00f  1
  31  2.3547485e+02 1.49e-08 2.90e-06  -8.6 2.49e+07 -18.3 1.00e+00 1.00e+00f  1
  32  2.4771819e+02 1.49e-08 1.45e-06  -8.6 4.42e+07 -18.8 1.00e+00 1.00e+00f  1
  33  2.5995789e+02 2.98e-08 7.24e-07  -8.6 7.84e+07 -19.3 1.00e+00 1.00e+00f  1
  34  2.7219319e+02 5.96e-08 3.62e-07  -8.6 1.39e+08 -19.7 1.00e+00 1.00e+00f  1
  35  2.8440212e+02 5.96e-08 1.82e-07  -8.6 2.16e+08 -20.0 1.00e+00 1.00e+00f  1
  36  2.9650073e+02 1.19e-07 9.21e-08  -8.6 2.50e+08 -20.0 1.00e+00 1.00e+00f  1
  37  3.0832577e+02 1.19e-07 4.69e-08  -8.6 2.55e+08 -20.0 1.00e+00 1.00e+00f  1
  38  3.1950929e+02 2.38e-07 2.38e-08  -8.6 2.42e+08 -20.0 1.00e+00 1.00e+00f  1
  39  3.2932585e+02 2.38e-07 1.14e-08  -8.6 3.31e+08 -20.0 1.00e+00 1.00e+00f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  40  3.3681949e+02 2.38e-07 4.58e-09  -8.6 4.26e+08 -20.0 1.00e+00 1.00e+00f  1
  41  3.4192630e+02 2.95e-07 1.80e-09  -8.6 4.30e+08 -20.0 1.00e+00 1.00e+00f  1
  42  3.4545689e+02 2.84e-07 8.66e-10  -8.6 3.88e+08 -20.0 1.00e+00 1.00e+00f  1
  43  3.4806621e+02 4.77e-07 4.58e-10  -8.6 3.43e+08 -20.0 1.00e+00 1.00e+00f  1
  44  3.5011537e+02 5.03e-07 2.43e-10  -8.6 3.06e+08 -20.0 1.00e+00 1.00e+00f  1
  45  3.5179669e+02 4.77e-07 1.22e-10  -8.6 2.77e+08 -20.0 1.00e+00 1.00e+00f  1
  46  3.5321985e+02 4.77e-07 5.58e-11  -8.6 2.55e+08 -20.0 1.00e+00 1.00e+00f  1
  47  3.5445240e+02 4.89e-07 2.40e-11  -8.6 2.38e+08 -20.0 1.00e+00 1.00e+00f  1

Number of Iterations....: 47

                                   (scaled)                 (unscaled)
Objective...............:  -3.5445239718699605e+02    3.5445239718699605e+02
Dual infeasibility......:   2.3959432454280738e-11    2.3959432454280738e-11
Constraint violation....:   4.8941001296043396e-07    4.8941001296043396e-07
Variable bound violation:   0.0000000000000000e+00    0.0000000000000000e+00
Complementarity.........:   0.0000000000000000e+00    0.0000000000000000e+00
Overall NLP error.......:   4.8941001296043396e-07    4.8941001296043396e-07


Number of objective function evaluations             = 84
Number of objective gradient evaluations             = 48
Number of equality constraint evaluations            = 84
Number of inequality constraint evaluations          = 0
Number of equality constraint Jacobian evaluations   = 1
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations             = 47
Total seconds in IPOPT                               = 16.889

This solution is not correct.
Do I need to tweak the optimizer parameters to get a more precise answer? How?

[pulsipher]

Log function objectives can be tricky for solvers to handle somethings if candidate solutions approach 0. You can try adding some bounds to your variables to see if that helps. The other thing to note is that Ipopt is a local solver, so it is not guaranteed to achieve the true (global) optimal solution for nonconvex problems. Hence you can try another nonlinear solver (https://jump.dev/JuMP.jl/dev/installation/#Supported-solvers), Alpine.jl might be a good open source choice.