Please read the first post of Please read: make it easier to help you - #81.
Use an @NLparameter for p:
model = Model(Ipopt.Optimizer)
@variable(model, x >= 0)
@NLparameter(model, p == 1)
f(x, p) = x + p
register(model, :f, 2, f; autodiff = true)
@NLobjective(model, Min, f(x, p))
julia> optimize!(model)
******************************************************************************
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 3.13.2, running with linear solver mumps.
NOTE: Other linear solvers might be more efficient (see Ipopt documentation).
Number of nonzeros in equality constraint Jacobian...: 0
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 0
Total number of variables............................: 1
variables with only lower bounds: 1
variables with lower and upper bounds: 0
variables with only upper bounds: 0
Total number of equality constraints.................: 0
Total number of inequality constraints...............: 0
inequality constraints with only lower bounds: 0
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 0
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 1.0100000e+00 0.00e+00 0.00e+00 0.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 1.0001000e+00 0.00e+00 9.90e-03 -8.0 9.90e-03 - 1.00e+00 1.00e+00f 1
2 1.0000010e+00 0.00e+00 1.01e-04 -10.0 1.01e-04 - 1.00e+00 9.80e-01f 1
3 9.9999999e-01 0.00e+00 9.90e-07 -11.0 9.90e-07 - 1.00e+00 1.00e+00f 1
4 9.9999999e-01 0.00e+00 9.00e-11 -11.0 9.00e-11 - 1.00e+00 1.00e+00f 1
Number of Iterations....: 4
(scaled) (unscaled)
Objective...............: 9.9999999000999995e-01 9.9999999000999995e-01
Dual infeasibility......: 8.9989682372504376e-11 8.9989682372504376e-11
Constraint violation....: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 9.9999109013750533e-12 9.9999109013750533e-12
Overall NLP error.......: 8.9989682372504376e-11 8.9989682372504376e-11
Number of objective function evaluations = 5
Number of objective gradient evaluations = 5
Number of equality constraint evaluations = 0
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 0
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 0
Total CPU secs in IPOPT (w/o function evaluations) = 1.509
Total CPU secs in NLP function evaluations = 0.022
EXIT: Optimal Solution Found.
julia> value(x)
0.0
julia> objective_value(model)
0.99999999001