StructuredOptimization.jl : parsing issue when adding constraints

Specific Domains Optimization (Mathematical)
1

Hi,

I’m trying to solve a modified LASSO where weights are constrained to be nonnegative, using StructuredOptimization.jl. The documentation suggests this should be possible using a code similar to the one below :

using StructuredOptimization

n = 5
p = 10
A = rand(n, p)
y = rand(n)

x = Variable(n)

@minimize ls(A*x-y) + norm(x, 1) st x >= 0.

This however gives me the following error message :
“Sorry, I cannot parse this problem for solver of type PANOC{Float64}”

Does someone (maybe @nantonel or @lostella ?) have any idea what is wrong with this ? Thanks anyway for developping this package which I have found extremly useful and easy to use aside this particular case :slight_smile:

2

Glad you’re enjoying the package! :grinning:

Unfortunately you cannot solve that type of problem at the moment…
See the this section of the documentation.

3

I’ll have a look at it! Thank you for your reply!

4

For this particular problem, I think the l_1 norm can be rewritten as sum(x) or 1^Tx (as x is non-negative) and absorbed into the smooth part of the objective. The problem could then be solved with a proximal method (though if your problem is small I’d recommend LBFGS-B).

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5

I was about to suggest the same:

using StructuredOptimization

n = 5
p = 10
A = rand(n, p)
y = rand(n)

x = Variable(p)

@minimize ls(A*x-y) + dot(ones(p), x) st x >= 0.0

should do the trick?

Edit: fixed the snippet after @nantonel’s suggestion

2 Likes
6

Sure ! I’m a bit ashamed to not have noticed this earlier ! Thank you all for your help :slight_smile:

7

well then, I’m even more ashamed! :rofl:

8

Just some minor correction to have the problem accepted:

n = 5
p = 10
A = rand(n, p)
y = rand(n)

x = Variable(p)

@minimize ls(A*x-y) + dot(ones(p),x) st x >= 0.0

that is currently dot needs inputs to be (::Array,::Variable) and x >= float(0).

1 Like
9

No one needs to feel shame – this is a textbook example of an XY Problem. And for readers, it’s a great reminder to keep this in mind.

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