[Ipopt] help diagnosing Ipopt error

[Jorge Fernández de Cossío Díaz]

I am using JuMP + Ipopt to solve a nonlinear constrained optimization
problem. The problem is of this form:

P = JuMP.Model()
JuMP. at variable(P, x0[j] ≤ x[j=1:N] ≤ x1[j])
JuMP. at variable(P, y0[j] ≤ y[j=1:M] ≤ y1[j])
JuMP. at variable(P, z0[j] ≤ z[j=1:M] ≤ z1[j])
JuMP. at variable(P, lambda ≥ 0)
JuMP. at variable(P, Q ≥ 0)
JuMP. at constraint(P, matrix * x .== lambda * b - y)
for i = 1:M
    JuMP. at NLconstraint(P, y[i] ≤ z[i] / (T[i] + z[i]))
    JuMP. at NLconstraint(P, z[i] == R[i] - y[i] * Q)
end
JuMP. at NLconstraint(P, lambda / prod{1. + z[i] / R2[i], i=1:M} - prod{z[i] /
(R3[i] + z[i]), i=1:M} - C ≥ 0)

where x0, x1, y0, ..., z1 are vectors previously defined, 'matrix' is a MxN
matrix, also previously defined, 'b' an M-vector, T, R, R2, R3 also
previously defined vectors.

I copied below the full Ipopt output containing the error I get when I try
to optimize this model. I have no clue of where to start looking for the
source of this error. Can someone point out common causes of this error, so
I can get started?


******************************************************************************
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 http://projects.coin-or.org/Ipopt
******************************************************************************

This is Ipopt version 3.12.1, running with linear solver mumps.
NOTE: Other linear solvers might be more efficient (see Ipopt
documentation).

Number of nonzeros in equality constraint Jacobian...:     1495
Number of nonzeros in inequality constraint Jacobian.:      501
Number of nonzeros in Lagrangian Hessian.............:    27107

Total number of variables............................:      505
                     variables with only lower bounds:      256
                variables with lower and upper bounds:      231
                     variables with only upper bounds:        1
Total number of equality constraints.................:      458
Total number of inequality constraints...............:      230
        inequality constraints with only lower bounds:        1
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:      229


Number of Iterations....: 0

Number of objective function evaluations             = 0
Number of objective gradient evaluations             = 1
Number of equality constraint evaluations            = 1
Number of inequality constraint evaluations          = 1
Number of equality constraint Jacobian evaluations   = 1
Number of inequality constraint Jacobian evaluations = 1
Number of Lagrangian Hessian evaluations             = 0
Total CPU secs in IPOPT (w/o function evaluations)   =      0.060
Total CPU secs in NLP function evaluations           =      0.004

EXIT: Invalid number in NLP function or derivative detected.
WARNING: Ipopt finished with status Invalid_Number_Detected
WARNING: Not solved to optimality, status: Error
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