Help diagnosing Ipopt error

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Jorge Fernández de Cossío Díaz

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May 12, 2016, 7:41:58 PM5/12/16

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

P = JuMP.Model()

JuMP.@variable(P, x0[j] ≤ x[j=1:N] ≤ x1[j])

JuMP.@variable(P, y0[j] ≤ y[j=1:M] ≤ y1[j])

JuMP.@variable(P, z0[j] ≤ z[j=1:M] ≤ z1[j])

JuMP.@variable(P, lambda ≥ 0)

JuMP.@variable(P, Q ≥ 0)

JuMP.@constraint(P, matrix * x .== lambda * b - y)

for i = 1:M

JuMP.@NLconstraint(P, y[i] ≤ z[i] / (T[i] + z[i]))

JuMP.@NLconstraint(P, z[i] == R[i] - y[i] * Q)

end

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)

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

Miles Lubin

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May 13, 2016, 8:25:43 AM5/13/16

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This error usually means that you haven't provided Ipopt with a starting point at which it can evaluate the constraints or objective. Try giving it a feasible starting point e.g.,