# Optimization of an univariate function using Optim.jl

**URL:** <https://discourse.julialang.org/t/optimization-of-an-univariate-function-using-optim-jl/123454>\
**Category:** Optimization (Mathematical)\
**Created:** [December 4, 2024, 1:43pm UTC](https://discourse.julialang.org/t/optimization-of-an-univariate-function-using-optim-jl/123454 "2024-12-04T13:43:41Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![Maucejo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/maucejo/32/39090_2.png) [@Maucejo](https://discourse.julialang.org/u/Maucejo)\
**Post date:** [December 4, 2024, 1:43pm UTC](https://discourse.julialang.org/t/optimization-of-an-univariate-function-using-optim-jl/123454/1 "2024-12-04T13:43:41Z")

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Dear all,

I am trying to deepen my knowledge of the `Optim.jl` package and in a near future of `Optimization.jl`.

In the course of my research, I have developed a method for estimating the noise in a signal. This methodology involves the resolution of a set of univariate optimization problems.

My first approach was to use the Brent’s method to solve the problem, since it is the indicated approach for this kind of problem. Below is a MWE (extracted from the documentation of `Optim.jl`), representative of the difficulties I am struggling with.

```julia
using Optim

f(x) = 2x^2 + 3x + 1

# Brent's method - Success
res = optimize(f, -2, 1)
xopt = Optim.minimizer(res)

# xopt = -0.75

```

Then I tried to use the Nelder-Mead method and it absolutely failed. Here is my attempt.

```julia
# First attempt
res2 = optimize(f, [0.]) # Error

# Second attempt
g(x) = @. 2x^2 + 3x + 1
res3 = optimize(g, [0.]) # Error

```

I think the problem is quite logical, if my understanding is correct, since the function to minimize must a scalar (Float64). However, when using Nelder-Mead, the initial must be a vector. Considering, I have tempted the following and more esoteric approach.

```julia
h(x) = (@. 2x^2 + 3x + 1)[1]
res4 = optimize(h, [0.])
xopt4 = Optim.minimizer(res4)[1]

# xopt4 = -0.7500000000000002

```

Although this approach is successful, it feels a bit unnatural.

My question is : Is there a more idiomatic way of minimizing univariate function using Nelder-Mead() or any other optimization technique (LBFGS, …) ?

Thank you !

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<div class="post-metadata">

**Author:** ![zdenek\_hurak](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/zdenek_hurak/32/53118_2.png) [@zdenek\_hurak](https://discourse.julialang.org/u/zdenek_hurak)\
**Post date:** [December 4, 2024, 5:47pm UTC](https://discourse.julialang.org/t/optimization-of-an-univariate-function-using-optim-jl/123454/2 "2024-12-04T17:47:52Z")

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I guess that in the univariate case there are more straightforward methods for optimization than the Nelder-Mead, essentially line search methods: [LineSearches.jl](https://github.com/JuliaNLSolvers/LineSearches.jl).

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**Author:** ![bertschi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bertschi/32/33462_2.png) [@bertschi](https://discourse.julialang.org/u/bertschi)\
**Post date:** [December 4, 2024, 6:01pm UTC](https://discourse.julialang.org/t/optimization-of-an-univariate-function-using-optim-jl/123454/3 "2024-12-04T18:01:56Z")

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What about

```julia
res2 = optimize(f ∘ only, [0.]) # ?

```

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<div class="post-metadata">

**Author:** ![Maucejo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/maucejo/32/39090_2.png) [@Maucejo](https://discourse.julialang.org/u/Maucejo)\
**Post date:** [December 5, 2024, 5:36am UTC](https://discourse.julialang.org/t/optimization-of-an-univariate-function-using-optim-jl/123454/4 "2024-12-05T05:36:57Z")

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Of course you’re right, but I wanted to test the interface to see to what extent I can write generic code for both univarita and multivariate optimization.

Thanks for pointing the LineSearches.jl.