# JuMP with Ipopt - Error "The equality constraints contain an invalid number"

Hi there,

I am trying to solve the following system of nonlinear equations

``````      using JuMP, Ipopt
c = Model(with_optimizer(Ipopt.Optimizer,max_cpu_time=500.0))
@variable(c,x)
@variable(c,y)
@NLconstraint(c,(1/x)*(2+(0.5)/(x-y)-y^2) == 0)
@NLconstraint(c,(1/(x^2))*(-2*y -(0.5)*(y/(x-y))+(1/3)*y^3+0.5*log(x-y)) == 0)
@NLconstraint(c, x >= y + 0.001)
optimize!(c)
``````

but I get an error message, “The equality constraints contain an invalid number”. I cannot understand what is being referred to.

Any hint would be most appreciated, thanks

x is allowed to be 0, so you have a divide by zero error with 1/x.

Ipopt assumes that your model is differentiable over the domain.

Hi there,

thanks for that. I did think about that: in fact, adding one more constraint

``````                    @NLconstraint(c, x >=  0.001)
``````

does not improve things much, what I am missing? Ipopt assumes the model is differentiable everywhere, but can this be relaxed via NL constraints?