# Conditional inside a function to be optimized

**URL:** <https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563>\
**Category:** Optimization (Mathematical)\
**Tags:** jump, optimization\
**Created:** [October 17, 2020, 10:41pm UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563 "2020-10-17T22:41:00Z")\
**Posts on this page:** 19\
**Page:** 1

<div class="post-metadata">

**Author:** ![danuzco](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/danuzco/32/18740_2.png) [@danuzco](https://discourse.julialang.org/u/danuzco)\
**Post date:** [October 17, 2020, 10:41pm UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/1 "2020-10-17T22:41:00Z")

</div>

I’m trying to maximize this function

```julia
function C_opt(s)
    
    pax, pby = OffsetArray( zeros(Float64, (2,2)), (0:1,0:1) ), OffsetArray( zeros(Float64, (2,2)), (0:1,0:1) )
    
    Cmax = 0
    for l=0:15
        pax[0,0], pax[0,1], pby[0,0], pby[0,1] = digits(l, base=2, pad=4)
        pax[1,0], pax[1,1], pby[1,0], pby[1,1] = 1- pax[0,0], 1- pax[0,1], 1- pby[0,0], 1- pby[0,1]
        
        C = 0
        j = 1 
        
        for i=0:15
            a,b,x,y = digits(i, base=2, pad=4)
            C += s[j]*pax[a,x]*pby[b,y]
            j += 1
        end
        C = C + s[j]*pax[0,0] + s[j+1]*pax[1,0]
        
        if Cmax > C
            Cmax = C
        end
        

    end
    
    return Cmax

end

model = Model(optimizer_with_attributes(Ipopt.Optimizer, "print_level" => 0));
@variable(model, -1 <= s[i = 1:18] <= 1, start = rand(Uniform(-1,1)) )
@objective(model, Max, C_opt(s) )

optimize!(model)
@show objective_value(model)

```

but I’m getting this error

MethodError: no method matching isless(::GenericAffExpr{Float64,VariableRef}, ::Int64)  
Closest candidates are:  
isless(!Matched::Missing, ::Any) at missing.jl:87  
isless(!Matched::AbstractFloat, ::Real) at operators.jl:167  
isless(!Matched::ForwardDiff.Dual{Tx,V,N} where N where V, ::Integer) where Tx at  
…

Commenting this lines

```julia
if Cmax > C
             Cmax = C
end

```

I get something, but it is not the right answer, that "if " statement has to be there

Thanks in advance!

---

<div class="post-metadata">

**Author:** ![Henrique\_Becker](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/henrique_becker/32/15443_2.png) [@Henrique\_Becker](https://discourse.julialang.org/u/Henrique_Becker)\
**Post date:** [October 17, 2020, 10:55pm UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/2 "2020-10-17T22:55:53Z")

</div>

First of all, welcome to our community!

Second, thanks for already taking your time to post the code inside triple backquotes.

Third, you are comparing a number (more specifically, `0 :: Int64`) with an expression that has model variables associated. These variables have not a defined value before you run the model, if these are run together with the model (I never used Ipopt), then your probably need to call the function `value` over the expression or, more probably, over the variables and then use the values instead to compute what you want. Ex.: if `s` is a vector of variables then `value.(s)` will get a vector of their values (as `Float64`), and then you can use them for your computation instead of the variables themselves.

---

<div class="post-metadata">

**Author:** ![danuzco](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/danuzco/32/18740_2.png) [@danuzco](https://discourse.julialang.org/u/danuzco)\
**Post date:** [October 17, 2020, 11:05pm UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/3 "2020-10-17T23:05:14Z")

</div>

Thanks for replying. I’m not sure of understanding your answer. `s` is certainly a vector, but that’s precisely the one I want to find, the vector that maximizes the function `C_opt(s)`. I tested the code with a similar function and it worked, and the it works in python with _minimize_ from _scipy.optimize_.

I don’t understand what’s the problem with the “if” inside the function.

---

<div class="post-metadata">

**Author:** ![Henrique\_Becker](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/henrique_becker/32/15443_2.png) [@Henrique\_Becker](https://discourse.julialang.org/u/Henrique_Becker)\
**Post date:** [October 17, 2020, 11:17pm UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/4 "2020-10-17T23:17:14Z")

</div>

If you do `@show typeof(s)` after the `@variable` you will see it is a `Vector` of `JuMP` variables, i.e., the unknowns you are trying to get to know the values which maximize the value of the objective function.

One thing I only perceived now is that you call `C_opt` in `@objective(model, Max, C_opt(s) )` I am not sure if this is what you want. `C_opt(s)` will evaluate the expression returned **before** the solver runs and, therefore, `s` does not have any values yet. So it seems to me to be wrong.

_You also said you removed the `if` statement and did not get the values you wanted_, but in this case you provided no objective function (in truth, you provided an objective function that is just the constant zero and, consequently, if the model finds any valid solution it will just stop).

_Maybe you meant `@objective(model, Max, C_opt)` so the `C_opt` is run every step of the optimization process?_ (Again, I never used a blackbox optimizer, so I do not know if this is the right syntx.) In this case, you probably want to return a computed value for the current solution, and we circle back to you needing to use `value` to extract the current values from the unknowns.

---

<div class="post-metadata">

**Author:** ![Henrique\_Becker](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/henrique_becker/32/15443_2.png) [@Henrique\_Becker](https://discourse.julialang.org/u/Henrique_Becker)\
**Post date:** [October 17, 2020, 11:21pm UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/5 "2020-10-17T23:21:09Z")

</div>

> [@danuzco](#):
>
> I don’t understand what’s the problem with the “if” inside the function.

> [@Henrique\_Becker](#):
>
> you are comparing a number (more specifically, `0 :: Int64` ) with an expression that has model variables associated. These variables have not a defined value before you run the model,

Basically, you are comparing an equation with unknowns (i.e., letters that may be replaced by any values inside a range) with zero. This is not defined. What you expected? That it returned `true` only if it is true for all values that the variables may assume? What is your expected result for `a <= 0` when `a` is defined like `-1 <= a <= 1`?

---

<div class="post-metadata">

**Author:** ![danuzco](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/danuzco/32/18740_2.png) [@danuzco](https://discourse.julialang.org/u/danuzco)\
**Post date:** [October 17, 2020, 11:25pm UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/7 "2020-10-17T23:25:35Z")

</div>

I understand your point here, but it’s no like the optimizer is generating solutions and passing that “provisional” vector `s` to the function?

---

<div class="post-metadata">

**Author:** ![Henrique\_Becker](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/henrique_becker/32/15443_2.png) [@Henrique\_Becker](https://discourse.julialang.org/u/Henrique_Becker)\
**Post date:** [October 17, 2020, 11:34pm UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/8 "2020-10-17T23:34:17Z")

</div>

Maybe the optimizer pass the vector of values already, I do not know. But you are not passing the function to the optimizer to discover that, you are passing to the optimizer the **return** of `C_opt` with the initial (without value) vector of variables `s`, if you want to pass function `C_opt` , then just pass it, not the results of its call.

---

<div class="post-metadata">

**Author:** ![danuzco](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/danuzco/32/18740_2.png) [@danuzco](https://discourse.julialang.org/u/danuzco)\
**Post date:** [October 18, 2020, 12:21am UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/9 "2020-10-18T00:21:13Z")

</div>

I’m expecting to obtain a numerical value. The only possible values that pax[…] and pby[…] can have are 0 and 1. Maybe this optimizer is not the right choice for this problem. As I said, I wrote the same code in python and it works. This function C\_opt is a function that I need to optimize a more complex problem, but in view that C\_opt was giving me problems I wanted to fix it first.

By the way, the right line above is C \> Cmax.

---

<div class="post-metadata">

**Author:** ![Henrique\_Becker](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/henrique_becker/32/15443_2.png) [@Henrique\_Becker](https://discourse.julialang.org/u/Henrique_Becker)\
**Post date:** [October 18, 2020, 1:13am UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/10 "2020-10-18T01:13:20Z")

</div>

I think Ipopt already receive the parameters as values (so you do not need to call `value`), and you can use the call notation you are using (i.e., `@objective(model, Max, C_opt(s) )`, because it is a macro and it uses some “dark magic” so its is not really calling `C_opt(s)` and passing the answe there). However, maybe what you want is `@NLobjective` instead of `@objective`, at least this is what occurs to me looking at [this example](https://jump.dev/JuMP.jl/v0.21.1/nlp/#Syntax-notes-1).

---

<div class="post-metadata">

**Author:** ![lmiq](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lmiq/32/18314_2.png) [@lmiq](https://discourse.julialang.org/u/lmiq)\
**Post date:** [October 18, 2020, 11:18am UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/11 "2020-10-18T11:18:26Z")

</div>

I think the problem is in the definition of the bounds. Try starting them like this:

```julia
julia> l = [-1 for i in 1:18] ; u = [1 for i in 1:18];

julia> @variable(model, l[i] <= s[i = 1:18] <= u[i], start = ... 

```

---

<div class="post-metadata">

**Author:** ![Henrique\_Becker](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/henrique_becker/32/15443_2.png) [@Henrique\_Becker](https://discourse.julialang.org/u/Henrique_Becker)\
**Post date:** [October 18, 2020, 12:17pm UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/12 "2020-10-18T12:17:19Z")

</div>

I thought that too, but danuzco says the code runs if he comments an unrelated `if` statement, so it does not appear to be so.

---

<div class="post-metadata">

**Author:** ![lmiq](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lmiq/32/18314_2.png) [@lmiq](https://discourse.julialang.org/u/lmiq)\
**Post date:** [October 18, 2020, 12:38pm UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/13 "2020-10-18T12:38:02Z")

</div>

The error disappears here with that change. It may be simply a casualty that s does not get projected on the bounds in that specific execution if the `if` is removed. One would need to see the exact iteration output of Ipopt to know what is going on.

---

<div class="post-metadata">

**Author:** ![danuzco](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/danuzco/32/18740_2.png) [@danuzco](https://discourse.julialang.org/u/danuzco)\
**Post date:** [October 18, 2020, 3:30pm UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/14 "2020-10-18T15:30:16Z")

</div>

Thanks for your answer. I’m trying to use this approach but I’m getting something wrong with the same code I was using. I’m even trying with this simple example I grabbed from [https://nbviewer.jupyter.org/github/jump-dev/JuMPTutorials.jl/blob/master/notebook/introduction/getting\_started\_with\_JuMP.ipynb](https://nbviewer.jupyter.org/github/jump-dev/JuMPTutorials.jl/blob/master/notebook/introduction/getting_started_with_JuMP.ipynb)

```julia
using JuMP
using GLPK

model = Model(GLPK.Optimizer)
@variable(model, x >= 0)
@variable(model, y >= 0)
@constraint(model, 6x + 8y >= 100)
@constraint(model, 7x + 12y >= 120)
@objective(model, Min, 12x + 20y)

optimize!(model)

@show value(x);
@show value(y);
@show objective_value(model);

```

MethodError: no method matching Model(::Type{GLPK.Optimizer})  
Closest candidates are:  
Model(::Any, !Matched::Symbol, !Matched::Any, !Matched::Any, !Matched::Any, !Matched::Any, !Matched::Any, !Matched::Int64, !Matched::Array{String,1}, !Matched::Array{String,1}, !Matched::Array{Float64,1}, !Matched::Array{Float64,1}, !Matched::Array{Symbol,1}, !Matched::Array{T,1}

can you see what’s wrong? this should work.

---

<div class="post-metadata">

**Author:** ![lmiq](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lmiq/32/18314_2.png) [@lmiq](https://discourse.julialang.org/u/lmiq)\
**Post date:** [October 18, 2020, 4:16pm UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/15 "2020-10-18T16:16:14Z")

</div>

Here that worked. Please be sure that you have restarted your Julia section (it may be that the model previously defined is interfering there, I don’t know):

```julia
julia> using JuMP

julia> using GLPK
[Info: Precompiling GLPK [60bf3e95-4087-53dc-ae20-288a0d20c6a6]

julia> model = Model(GLPK.Optimizer)
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: EMPTY_OPTIMIZER
Solver name: GLPK

julia> @variable(model, x >= 0)
x

julia> @variable(model, y >= 0)
y

julia> @constraint(model, 6x + 8y >= 100)
6 x + 8 y ≥ 100.0

julia> @constraint(model, 7x + 12y >= 120)
7 x + 12 y ≥ 120.0

julia> @objective(model, Min, 12x + 20y)
12 x + 20 y

julia> optimize!(model)

julia> @show value(x);
value(x) = 14.999999999999993

julia> @show value(y);
value(y) = 1.2500000000000047

julia> @show objective_value(model);
objective_value(model) = 205.0

julia> 

```

---

<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 18, 2020, 8:32pm UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/16 "2020-10-18T20:32:19Z")

</div>

There are a few comments leading you astray in this thread, so let me summarize.

- Your problem is nonlinear. You need to use the nonlinear interface for JuMP. In particular, you need to use a user-defined function: [https://jump.dev/JuMP.jl/stable/nlp/#User-defined-Functions-1](https://jump.dev/JuMP.jl/stable/nlp/#User-defined-Functions-1).
- The nonlinear interface requires functions with scalar inputs, so `s` can’t be a vector input. [Read this suggested work-around.](https://jump.dev/JuMP.jl/stable/nlp/#User-defined-functions-with-vector-inputs-1)
- @Henrique_Becker is correct that `@objective(model, Max, C_opt(s)` evaluates this function with the arguments as JuMP variables _before_ passing it to the solver. This is a little confusing, but is very helpful in some cases.
- I don’t understand the need for `OffSetArray`, but it looks like your nonlinearity is just the single `max(0, C)`? Due to nondifferentiability and the large flat area, Ipopt tends to struggle with this. You might get a local optima.
- There is nothing wrong with how you have defined `@variable`.
- Your issue with `Model(GLPK.Optimizer)` is because you are using an old version of JuMP, although I think you’ve fixed this in [another issue](https://discourse.julialang.org/t/getting-methoderror-no-method-matching-model-when-initializing-models-on-jump/43647/7).

---

<div class="post-metadata">

**Author:** ![danuzco](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/danuzco/32/18740_2.png) [@danuzco](https://discourse.julialang.org/u/danuzco)\
**Post date:** [October 18, 2020, 8:51pm UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/17 "2020-10-18T20:51:12Z")

</div>

@odow @Henrique_Becker @lmiq Thank you guys for helping me with this issue, I’ll try to follow your suggestions and see if I can make it work.

---

<div class="post-metadata">

**Author:** ![Humphrey\_Lee](https://avatars.discourse-cdn.com/v4/letter/h/a88e4f/32.png) [@Humphrey\_Lee](https://discourse.julialang.org/u/Humphrey_Lee)\
**Post date:** [April 28, 2021, 7:52am UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/18 "2021-04-28T07:52:10Z")

</div>

@danuzco Have you found solution to this problem? If yes, would you please share it for general and greater community learning?

---

<div class="post-metadata">

**Author:** ![cvanaret](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cvanaret/32/11594_2.png) [@cvanaret](https://discourse.julialang.org/u/cvanaret)\
**Post date:** [April 28, 2021, 8:55am UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/19 "2021-04-28T08:55:50Z")

</div>

I obviously missed the action, but let me suggest a basic reformulation that handles this:

```julia
if Cmax > C
   Cmax = C
end

```

The modeling “trick” consists in introducing an optimization variable C bounded by Cmax and introducing the equality constraint C\_{opt}(s) - C = 0 that synchronizes both values at the optimum.

---

<div class="post-metadata">

**Author:** ![Humphrey\_Lee](https://avatars.discourse-cdn.com/v4/letter/h/a88e4f/32.png) [@Humphrey\_Lee](https://discourse.julialang.org/u/Humphrey_Lee)\
**Post date:** [April 28, 2021, 9:18am UTC](https://discourse.julialang.org/t/conditional-inside-a-function-to-be-optimized/48563/20 "2021-04-28T09:18:41Z")

</div>

Interesting remarks. I will look at reparameterization of my problem. Thanks.