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lostella
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Feb 21, 2025
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| Return the indicator of the unit simplex | ||
| ```math | ||
| S = \\left\\{ x : x \\geq 0, \\sum_i x_i \\leq a \\right\\}. |
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Hmmm yeah, naming is tough here. Would this set be the convex hull of S u {0}, where S is that of IndSimplex? (i.e. with equality on the sum)
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Well, the origin 0 \in R^k is the projection to R^k of e_{k+1} \in R^{k+1}. So I guess this set is the projection to R^k of the k-simplex (which lives in R^{k+1} originally). If so, this could suggest a better name maybe.
Am I making sense? Works in my mind for k=2 at least (hehe).
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Yes exactly that's one way to define it
…On Fri, Feb 21, 2025, 19:18 Lorenzo Stella ***@***.***> wrote:
***@***.**** commented on this pull request.
------------------------------
In src/functions/indSimplex.jl
<#150 (comment)>
:
> @@ -107,3 +107,49 @@ function prox_naive(f::IndSimplex, x, gamma)
end
return v, R(0)
end
+
+"""
+ IndUnitSimplex(a=1.0)
+
+Return the indicator of the unit simplex
+```math
+S = \\left\\{ x : x \\geq 0, \\sum_i x_i \\leq a \\right\\}.
Hmmm yeah, naming is tough here. Would this set be the convex hull of S u
{0}, where S is that of IndSimplex? (i.e. with equality on the sum)
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Couldn't find a better name, that's the one we use in FrankWolfe.jl.
Having a dedicated prox avoids having to create a n+1-dimensional simplex