JuMP constraint MethodError

Specific Domains Optimization (Mathematical)
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1

I’ve been trying to use a constraint that uses Distribution.cdf() in optimization using JuMP. An example of this usage would be similar to the below code.

model = JuMP.Model(NLopt.Optimizer);
set_optimizer_attribute(model, "algorithm", :LD_SLSQP);

@variable(model, x[1:11]);
@constraint(model, c2, Distributions.cdf(Normal(),x[1]) >= 0);

But this produces the error

ERROR: MethodError: no method matching cdf(::Normal{Float64}, ::VariableRef)

Closest candidates are:
  cdf(::UnivariateDistribution, ::AbstractArray)
   @ Distributions deprecated.jl:103
  cdf(::Normal, ::Real)
   @ Distributions C:\Users\gperera@ltu.edu.au\.julia\packages\Distributions\SUTV1\src\univariates.jl:637

Stacktrace:
 [1] macro expansion
   @ C:\Users\gperera@ltu.edu.au\.julia\packages\MutableArithmetics\NIXlP\src\rewrite.jl:321 [inlined]
 [2] macro expansion
   @ C:\Users\gperera@ltu.edu.au\.julia\packages\JuMP\D44Aq\src\macros.jl:717 [inlined]
 [3] top-level scope
   @ Untitled-1:34

Any help would be appreciated! Thanks!

2

You cannot use arbitrary nonlinear functions with JuMP.

See Should you use JuMP? · JuMP

If you can provide the analytic gradient of the function with respect to your variables then you could use a user-defined operator: Nonlinear Modeling · JuMP