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Add dual in RelativeEntropyCone docstring #1018

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chriscoey merged 2 commits into from
Feb 12, 2020
Merged

Add dual in RelativeEntropyCone docstring #1018

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Add dual in RelativeEntropyCone docstring
blegat Feb 8, 2020
6d57269
Add expression with log
blegat Feb 9, 2020
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6 changes: 6 additions & 0 deletions src/sets.jl
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Expand Up @@ -326,6 +326,12 @@ end
RelativeEntropyCone(dimension)

The relative entropy cone ``\\{ (u, v, w) \\in \\mathbb{R}^{1+2n} : u \\ge \\sum_{i=1}^n w_i \\log (\\frac{w_i}{v_i}), v_i \\ge 0, w_i \\ge 0 \\}`` of dimension `dimension```{}=2n+1``.

### Duality note

The dual of the relative entropy cone is
``\\{ (u, v, w) \\in \\mathbb{R}^{1+2n} : \\forall i, -u \\exp (v_i/u) \\le \\exp(1) w_i, u < 0 \\}`` of dimension `dimension```{}=2n+1``.
Note that the inequality is rewritten in terms of ``\\log`` as follows: ``v_i \\le u (\\log(w_i/-u) + 1)``.
"""
struct RelativeEntropyCone <: AbstractVectorSet
dimension::Int
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