# Optim.jl optimize 2 variable function with initial boundaries

I’m struggling to accomplish a basic task with Optim.
Let’s say I defined a function `f(a,x,y) = a + x^2 + y^2`. I want to minimize this function given initial boundaries: `x0 = [-10, 10]`, `y0 = [-10, 10]` and `a = 10, as constant`.

What do you mean by “initial boundary”? Are you looking for the minimum value of `f` within those bounds?

Yes. I want the optimizer to find the minimum value of `f` for `x, y` within the bounds, as well as return the corresponding `x, y` values.

Have you tried this?

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You can also use ProximalAlgorithms, see this example.

Note that the linked documentation refers to the `master` branch (a new release will be coming soon, which will then be covered by the documentation).

For fast convergence to high accuracy you can replace the `ffb` algorithm from the example with something like

``````ProximalAlgorithms.PANOC(verbose=true)
``````

(here is the relevant documentation for the algorithm)

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Thank you, but the docs don’t specify exactly how to handle multiple variables.

You can use a vector of length 2 as variable: in your example, you’ll be optimizing `f(x) = x^2 + x^2`.

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