<div dir="ltr"><span style="font-family:Arial,Helvetica,sans-serif;font-size:13px">I am using JuMP + Ipopt to solve a nonlinear constrained optimization problem. The problem is of this form:</span><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px"><br></div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px"><div style="margin:0px;padding:0px;border:0px">P = JuMP.Model()</div><div style="margin:0px;padding:0px;border:0px">JuMP.@variable(P, x0[j] ≤ x[j=1:N] ≤ x1[j])<br></div><div style="margin:0px;padding:0px;border:0px">JuMP.@variable(P, y0[j] ≤ y[j=1:M] ≤ y1[j])<br></div><div style="margin:0px;padding:0px;border:0px">JuMP.@variable(P, z0[j] ≤ z[j=1:M] ≤ z1[j])</div><div style="margin:0px;padding:0px;border:0px">JuMP.@variable(P, lambda ≥ 0)</div><div style="margin:0px;padding:0px;border:0px">JuMP.@variable(P, Q ≥ 0)</div><div style="margin:0px;padding:0px;border:0px">JuMP.@constraint(P, matrix * x .== lambda * b - y)</div><div style="margin:0px;padding:0px;border:0px">for i = 1:M</div><div style="margin:0px;padding:0px;border:0px">    JuMP.@NLconstraint(P, y[i] ≤ z[i] / (T[i] + z[i]))</div><div style="margin:0px;padding:0px;border:0px">    JuMP.@NLconstraint(P, z[i] == R[i] - y[i] * Q)</div><div style="margin:0px;padding:0px;border:0px">end</div><div style="margin:0px;padding:0px;border:0px">JuMP.@NLconstraint(P, lambda / prod{1. + z[i] / R2[i], i=1:M} - prod{z[i] / (R3[i] + z[i]), i=1:M} - C ≥ 0)</div></div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px"><br></div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">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.</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px"><br></div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">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?</div><div><br></div><div><br></div><div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">******************************************************************************</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">This program contains Ipopt, a library for large-scale nonlinear optimization.</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px"> Ipopt is released as open source code under the Eclipse Public License (EPL).</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">         For more information visit <a href="http://projects.coin-or.org/Ipopt" target="_blank" rel="nofollow" style="margin:0px;padding:0px;border:0px;text-decoration:none;color:rgb(102,17,204)">http://projects.coin-or.org/Ipopt</a></div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">******************************************************************************</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px"><br></div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">This is Ipopt version 3.12.1, running with linear solver mumps.</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">NOTE: Other linear solvers might be more efficient (see Ipopt documentation).</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px"><br></div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">Number of nonzeros in equality constraint Jacobian...:     1495</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">Number of nonzeros in inequality constraint Jacobian.:      501</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">Number of nonzeros in Lagrangian Hessian.............:    27107</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px"><br></div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">Total number of variables............................:      505</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">                     variables with only lower bounds:      256</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">                variables with lower and upper bounds:      231</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">                     variables with only upper bounds:        1</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">Total number of equality constraints.................:      458</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">Total number of inequality constraints...............:      230</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">        inequality constraints with only lower bounds:        1</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">   inequality constraints with lower and upper bounds:        0</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">        inequality constraints with only upper bounds:      229</div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px"><br></div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px"><br></div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px">Number of Iterations....: 0</div></div><div><br></div><div><div style="margin:0px;padding:0px;border:0px;font-family:Arial,Helvetica,sans-serif;font-size:13px"><div style="margin:0px;padding:0px;border:0px">Number of objective function evaluations             = 0</div><div style="margin:0px;padding:0px;border:0px">Number of objective gradient evaluations             = 1</div><div style="margin:0px;padding:0px;border:0px">Number of equality constraint evaluations            = 1</div><div style="margin:0px;padding:0px;border:0px">Number of inequality constraint evaluations          = 1</div><div style="margin:0px;padding:0px;border:0px">Number of equality constraint Jacobian evaluations   = 1</div><div style="margin:0px;padding:0px;border:0px">Number of inequality constraint Jacobian evaluations = 1</div><div style="margin:0px;padding:0px;border:0px">Number of Lagrangian Hessian evaluations             = 0</div><div style="margin:0px;padding:0px;border:0px">Total CPU secs in IPOPT (w/o function evaluations)   =      0.060</div><div style="margin:0px;padding:0px;border:0px">Total CPU secs in NLP function evaluations           =      0.004</div><div style="margin:0px;padding:0px;border:0px"><br></div><div style="margin:0px;padding:0px;border:0px">EXIT: Invalid number in NLP function or derivative detected.</div><div style="margin:0px;padding:0px;border:0px">WARNING: Ipopt finished with status Invalid_Number_Detected</div><div style="margin:0px;padding:0px;border:0px">WARNING: Not solved to optimality, status: Error</div><div><br></div></div></div></div>