# How to add a constraint in a JuMP model using the obj function of another JuMP model

**URL:** <https://discourse.julialang.org/t/how-to-add-a-constraint-in-a-jump-model-using-the-obj-function-of-another-jump-model/29432>\
**Category:** Optimization (Mathematical)\
**Created:** [October 3, 2019, 4:55am UTC](https://discourse.julialang.org/t/how-to-add-a-constraint-in-a-jump-model-using-the-obj-function-of-another-jump-model/29432 "2019-10-03T04:55:49Z")\
**Posts on this page:** 9\
**Page:** 1

<div class="post-metadata">

**Author:** ![Mahbubar06](https://avatars.discourse-cdn.com/v4/letter/m/f07891/32.png) [@Mahbubar06](https://discourse.julialang.org/u/Mahbubar06)\
**Post date:** [October 3, 2019, 4:55am UTC](https://discourse.julialang.org/t/how-to-add-a-constraint-in-a-jump-model-using-the-obj-function-of-another-jump-model/29432/1 "2019-10-03T04:55:49Z")

</div>

Hello,  
I have the following JuMP model:

```julia
using JuMP
using MathProgBase
using Ipopt
model=Model(solver=IpoptSolver())
@variable(model, -100 <= x[1:5] <=100)
@constraint(model, sum(x[i] for i in 1:5) <= 50)
@NLconstraint(model, sum(x[i]^2 for i in 1:3) <= 50)
@NLobjective(model, Min, sum(x[i]^2 for i in 1:5))

```

I get the objective expression from the above model as below:

```julia
d = JuMP.NLPEvaluator(model)
MathProgBase.initialize(d, [:ExprGraph])
obj_expr=MathProgBase.obj_expr(d)

```

Now, I have a new model like this:

```julia
m=Model(solver=IpoptSolver())
@variable(m, -100 <= x[i=1:6] <= 100)
@constraint(m, sum(x[i] for i in 1:5) <=100)
@NLconstraint(m, sum(x[i]^2 for i in 1:5)<= 100)
@objectve(m, Min, sum(x[i] for i in 1:6))

```

And in the model “m” I need to add the following constraint:

```julia
JuMP.addNLconstraint(m, x[6]>= obj_expr)
or
JuMP.addNLconstraint(m, x[6]>=sum(x[i]^2 for i in 1:5) )

```

I have tried the following way:

```julia
expr=:(x[6]>=$(obj_expr))
JuMP.addNLconstraint(m, expr)

```

But it did not work. Can anyone help me with finding a way to add the constraint in model “m”. Thank you.  
NOTE: I am using JuMPv0.18 and MathProgBase

---

<div class="post-metadata">

**Author:** ![leethargo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/leethargo/32/6004_2.png) [@leethargo](https://discourse.julialang.org/u/leethargo)\
**Post date:** [October 3, 2019, 9:43am UTC](https://discourse.julialang.org/t/how-to-add-a-constraint-in-a-jump-model-using-the-obj-function-of-another-jump-model/29432/2 "2019-10-03T09:43:53Z")

</div>

> [@Mahbubar06](#):
>
> But it did not work. Can anyone help me with finding a way to add the constraint in model “m”. Thank you.

Could you please elaborate? Did get an error message?

> [@Mahbubar06](#):
>
> NOTE: I am using JuMPv0.18 and MathProgBase

Do you have to use these versions, or could you upgrade to JuMP & MOI?

---

<div class="post-metadata">

**Author:** ![Mahbubar06](https://avatars.discourse-cdn.com/v4/letter/m/f07891/32.png) [@Mahbubar06](https://discourse.julialang.org/u/Mahbubar06)\
**Post date:** [October 3, 2019, 3:18pm UTC](https://discourse.julialang.org/t/how-to-add-a-constraint-in-a-jump-model-using-the-obj-function-of-another-jump-model/29432/3 "2019-10-03T15:18:49Z")

</div>

my process did not work because I got the following error message:

```julia
julia> exp= :(x[6]>= $(obj_expr))
:(x[6] >= x[1] ^ 2.0 + x[2] ^ 2.0 + x[3] ^ 2.0 + x[4] ^ 2.0 + x[5] ^ 2.0)

julia> JuMP.addNLconstraint(m, exp)
ERROR: Unrecognized expression x[6]. JuMP variable objects and input coefficients should be spliced directly into expressions.
Stacktrace:
 [1] spliceref at C:\Users\mahbu\.julia\packages\JuMP\I7whV\src\parsenlp.jl:270 [inlined]
 [2] (::getfield(JuMP, Symbol("##138#139")){Model})(::Expr) at C:\Users\mahbu\.julia\packages\JuMP\I7whV\src\parsenlp.jl:272
 [3] iterate at .\generator.jl:47 [inlined]
 [4] collect_to!(::Array{Symbol,1}, ::Base.Generator{Array{Any,1},getfield(JuMP, Symbol("##138#139")){Model}}, ::Int64, ::Int64) at .\array.jl:651
 [5] collect_to_with_first!(::Array{Symbol,1}, ::Symbol, ::Base.Generator{Array{Any,1},getfield(JuMP, Symbol("##138#139")){Model}}, ::Int64) at .\array.jl:630
 [6] _collect(::Array{Any,1}, ::Base.Generator{Array{Any,1},getfield(JuMP, Symbol("##138#139")){Model}}, ::Base.EltypeUnknown, ::Base.HasShape{1}) at .\array.jl:624
 [7] collect_similar(::Array{Any,1}, ::Base.Generator{Array{Any,1},getfield(JuMP, Symbol("##138#139")){Model}}) at .\array.jl:548
 [8] map(::Function, ::Array{Any,1}) at .\abstractarray.jl:2073
 [9] spliceref at C:\Users\mahbu\.julia\packages\JuMP\I7whV\src\parsenlp.jl:272 [inlined]
 [10] JuMP.NonlinearExprData(::Model, ::Expr) at C:\Users\mahbu\.julia\packages\JuMP\I7whV\src\parsenlp.jl:261
 [11] addNLconstraint(::Model, ::Expr) at C:\Users\mahbu\.julia\packages\JuMP\I7whV\src\nlp.jl:1439
 [12] top-level scope at none:0

```

And for the JuMP version and MathProgBase, I do want to upgrade to JuMPv0.20 and MathOptInterface but for some time I need to bear with the versions I am using. I am sorry for your inconvenience with the older versions. Thank you.

---

<div class="post-metadata">

**Author:** ![leethargo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/leethargo/32/6004_2.png) [@leethargo](https://discourse.julialang.org/u/leethargo)\
**Post date:** [October 3, 2019, 4:10pm UTC](https://discourse.julialang.org/t/how-to-add-a-constraint-in-a-jump-model-using-the-obj-function-of-another-jump-model/29432/4 "2019-10-03T16:10:45Z")

</div>

I’m not sure about the error message, but why don’t you

```julia
@NLconstraint(m, x[6]>= obj_expr)

```

to avoid some macro/quoting/expr issue.

I’m not sure whether that will work either, because the variable objects in JuMP contain references to the model in which they are created, right?

---

<div class="post-metadata">

**Author:** ![leethargo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/leethargo/32/6004_2.png) [@leethargo](https://discourse.julialang.org/u/leethargo)\
**Post date:** [October 3, 2019, 4:12pm UTC](https://discourse.julialang.org/t/how-to-add-a-constraint-in-a-jump-model-using-the-obj-function-of-another-jump-model/29432/5 "2019-10-03T16:12:31Z")

</div>

Also, is the code you posted now just a simplified example? For quadratic expressions you could also use the `@constraint` macro, right?

---

<div class="post-metadata">

**Author:** ![Mahbubar06](https://avatars.discourse-cdn.com/v4/letter/m/f07891/32.png) [@Mahbubar06](https://discourse.julialang.org/u/Mahbubar06)\
**Post date:** [October 3, 2019, 4:17pm UTC](https://discourse.julialang.org/t/how-to-add-a-constraint-in-a-jump-model-using-the-obj-function-of-another-jump-model/29432/6 "2019-10-03T16:17:55Z")

</div>

```julia
@NLconstraint(m, x[6]>= obj_expr)

```

the above line gives the following error:

```julia
julia> @NLconstraint(m,x[6]>= obj_exp)
ERROR: Unexpected object x[6] >= x[1] ^ 2.0 + x[2] ^ 2.0 + x[3] ^ 2.0 + x[4] ^ 2.0 + x[5] ^ 2.0 in nonlinear expression.
Stacktrace:
 [1] parseNLExpr_runtime(::Model, ::Expr, ::Array{ReverseDiffSparse.NodeData,1}, ::Int64, ::Array{Float64,1}) at
C:\Users\mahbu\.julia\packages\JuMP\I7whV\src\parsenlp.jl:207
 [2] top-level scope at C:\Users\mahbu\.julia\packages\JuMP\I7whV\src\parsenlp.jl:249
 [3] top-level scope at C:\Users\mahbu\.julia\packages\JuMP\I7whV\src\macros.jl:1352

```

And your are right the obj\_expr expression has variables which are referenced to the model “model”. So how could I dereference the obj\_expr to the variables of model “m”?

---

<div class="post-metadata">

**Author:** ![Mahbubar06](https://avatars.discourse-cdn.com/v4/letter/m/f07891/32.png) [@Mahbubar06](https://discourse.julialang.org/u/Mahbubar06)\
**Post date:** [October 3, 2019, 4:30pm UTC](https://discourse.julialang.org/t/how-to-add-a-constraint-in-a-jump-model-using-the-obj-function-of-another-jump-model/29432/7 "2019-10-03T16:30:45Z")

</div>

But even if I did dereferance the obj\_expr with the model “m” variables I still get error messages. The code I used for dereferencing is the following:

```julia
#Used from https://github.com/lanl-ansi/Alpine.jl
function expr_dereferencing!(expr, m)
    for i in 2:length(expr.args)
        if isa(expr.args[i], Union{Float64,Int64})
            k = 0
        elseif expr.args[i].head == :ref
            @assert isa(expr.args[i].args[2], Int)
            expr.args[i] = Variable(m, expr.args[i].args[2])
        elseif expr.args[i].head == :call
            expr_dereferencing!(expr.args[i], m)
        else
            error("expr_dereferencing :: Unexpected term in expression tree.")
        end
    end
end

```

And the error message is the following:

```julia
julia> expr_dereferencing!(obj_expr, m)
julia> exp= :(x[6]>= $(obj_expr))
:(x[6] >= x[1] ^ 2.0 + x[2] ^ 2.0 + x[3] ^ 2.0 + x[4] ^ 2.0 + x[5] ^ 2.0)

julia> JuMP.addNLconstraint(m, exp)
ERROR: Unrecognized expression x[6]. JuMP variable objects and input coefficients should be spliced directly into expressions.
Stacktrace:
 [1] spliceref at C:\Users\mahbu\.julia\packages\JuMP\I7whV\src\parsenlp.jl:270 [inlined]
 [2] (::getfield(JuMP, Symbol("##138#139")){Model})(::Expr) at C:\Users\mahbu\.julia\packages\JuMP\I7whV\src\parsenlp.jl:272
 [3] iterate at .\generator.jl:47 [inlined]
 [4] collect_to!(::Array{Symbol,1}, ::Base.Generator{Array{Any,1},getfield(JuMP, Symbol("##138#139")){Model}}, ::Int64, ::Int64) at .\array.jl:651
 [5] collect_to_with_first!(::Array{Symbol,1}, ::Symbol, ::Base.Generator{Array{Any,1},getfield(JuMP, Symbol("##138#139")){Model}}, ::Int64) at .\array.jl:630
 [6] _collect(::Array{Any,1}, ::Base.Generator{Array{Any,1},getfield(JuMP, Symbol("##138#139")){Model}}, ::Base.EltypeUnknown, ::Base.HasShape{1}) at .\array.jl:624
 [7] collect_similar(::Array{Any,1}, ::Base.Generator{Array{Any,1},getfield(JuMP, Symbol("##138#139")){Model}}) at .\array.jl:548
 [8] map(::Function, ::Array{Any,1}) at .\abstractarray.jl:2073
 [9] spliceref at C:\Users\mahbu\.julia\packages\JuMP\I7whV\src\parsenlp.jl:272 [inlined]
 [10] JuMP.NonlinearExprData(::Model, ::Expr) at C:\Users\mahbu\.julia\packages\JuMP\I7whV\src\parsenlp.jl:261
 [11] addNLconstraint(::Model, ::Expr) at C:\Users\mahbu\.julia\packages\JuMP\I7whV\src\nlp.jl:1439
 [12] top-level scope at none:0

```

---

<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:** [October 3, 2019, 8:13pm UTC](https://discourse.julialang.org/t/how-to-add-a-constraint-in-a-jump-model-using-the-obj-function-of-another-jump-model/29432/8 "2019-10-03T20:13:06Z")

</div>

See the docs: [Nonlinear Modeling · JuMP](https://www.juliaopt.org/JuMP.jl/v0.20.0/nlp/#Raw-expression-input-1)

As it says, the variables need to be directly spliced into the expressions. So instead of

```nohighlight
exp = :(x[6])

```

you need

```nohighlight
exp = :($(x[6]))

```

---

<div class="post-metadata">

**Author:** ![Mahbubar06](https://avatars.discourse-cdn.com/v4/letter/m/f07891/32.png) [@Mahbubar06](https://discourse.julialang.org/u/Mahbubar06)\
**Post date:** [October 3, 2019, 10:10pm UTC](https://discourse.julialang.org/t/how-to-add-a-constraint-in-a-jump-model-using-the-obj-function-of-another-jump-model/29432/9 "2019-10-03T22:10:33Z")

</div>

Thank you @odow. You have solved my problem.