Optim.jl - How to find local maxima of multivariate function

Specific Domains Optimization (Mathematical)
1

Pardon my ignorance (if you’ve seen any recent posts of mine you’ll know I’ve been studying calculus lately) but I’m trying to understand how to find local maxima of a multivariate function with Optim.jl. Given the following function, it’s pretty easy to pick a starting point and let Optim work its magic to find local minima:

using Optim
using Plots
using Plots.PlotMeasures
pyplot(size=(1200,600))

f(x,y) = -5*x*y*exp(-x^2-y^2)
res = optimize(x -> f(x[1],x[2]), [1.0,1.0])
res2 = optimize(x -> f(x[1],x[2]), [-0.75,-0.75])

# Contour plot with local minima added
p = contour(
    x,
    y,
    z,
    color=:blues,
    legend=false,
    xlabel="x",
    ylabel="y"
)
plot!([Optim.minimizer(res)[1]], [Optim.minimizer(res)[2]], marker=:circle)
plot!([Optim.minimizer(res2)[1]], [Optim.minimizer(res2)[2]], marker=:circle)

local_minima
local_minima1200×600 101 KB

In this case, I can obviously just use the same values from res and res2 by switching the sign for the y value (-(Optim.minimizer(res)[2]) but is there a way to have it find local maxima just like it does for local minima? The docs seem to only discuss minimizing functions.

2

Multiply the objective be -1.

Maximizing f(x) is the same as minimizing -f(x).

2 Likes
3

Thanks! I actually did that after realizing myself it was the same. It would be nice to have a keyword argument that allows you to tell it to maximize rather than minimize but maybe there’s a good reason why that doesn’t exist.

4

Instead, I often wish that the function name was minimize instead of optimize, so that I don’t have to keep looking up the docs (each library does something different).

Then

maximize(f, args...) = minimize(x -> -f(x), args...)

would be a trivial wrapper (of course for AD etc it would be more complicated).

6 Likes