# How to register a function with parameter in JuMP

**URL:** <https://discourse.julialang.org/t/how-to-register-a-function-with-parameter-in-jump/45457>\
**Category:** Optimization (Mathematical)\
**Tags:** question, jump\
**Created:** [August 24, 2020, 2:54pm UTC](https://discourse.julialang.org/t/how-to-register-a-function-with-parameter-in-jump/45457 "2020-08-24T14:54:42Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![Behemoth-s](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/behemoth-s/32/17428_2.png) [@Behemoth-s](https://discourse.julialang.org/u/Behemoth-s)\
**Post date:** [August 24, 2020, 2:54pm UTC](https://discourse.julialang.org/t/how-to-register-a-function-with-parameter-in-jump/45457/1 "2020-08-24T14:54:43Z")

</div>

Here I have some variables and parameters

```julia
model = Model(Ipopt.Optimizer)
@variable(model, x[1:2])
p = [4, 6]

```

I want to register a function with parameter in JuMP to do something like this bellow.

```julia
function f(x, p)
    return (x - p)^2
end

register(model,:f, 2,f, ∇f)

@NLobjective(model, Min, sum(f(x[i], p[i]) for i in 1:2))

```

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [August 25, 2020, 1:07am UTC](https://discourse.julialang.org/t/how-to-register-a-function-with-parameter-in-jump/45457/2 "2020-08-25T01:07:09Z")

</div>

Please read the first post of [Please read: make it easier to help you - #81](https://discourse.julialang.org/t/psa-make-it-easier-to-help-you/14757/81).

Use an `@NLparameter` for `p`:

```nohighlight
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

```

---

<div class="post-metadata">

**Author:** ![Behemoth-s](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/behemoth-s/32/17428_2.png) [@Behemoth-s](https://discourse.julialang.org/u/Behemoth-s)\
**Post date:** [August 25, 2020, 2:10am UTC](https://discourse.julialang.org/t/how-to-register-a-function-with-parameter-in-jump/45457/3 "2020-08-25T02:10:25Z")

</div>

> [@odow](#):
>
> `objective_value`

Thanks a lot for your solution. It works well.  
Also in appreciation of your advice, I will update my question.

```julia
model = Model(optimizer_with_attributes(Ipopt.Optimizer))
p0 = [4,6]
@variable(model,x[1:2])
@NLparameter(model, p[i in 1:2] == p0[i])

function f(x, p)
    return (x - p)^2
end

function ∇f(g, x, p)
    g[1] = 2 * x - 2 * p
    # g[2] = 2 * p - 2 * x
end

register(model,:f, 2,f, ∇f)
@NLobjective(model, Min, sum(f(x[i], p[i]) for i in 1:2))
optimize!(model)
value.(x)
--------------------------------------------------------
EXIT: Optimal Solution Found.
2-element Array{Float64,1}:
 4.0
 6.0

```