Add the PSD cone

[blegat]

Scaled PSD cones are used by Mosek and SCS.
Unscaled PSD cones are used by SDPA, CSDP and DSDP.

[mlubin]

I'd prefer to have two separate cones for scaled and unscaled.

[blegat]

What would be the names then :-P UnscaledPositiveSemidefiniteCone and ScaledPositiveSemidefiniteCone ?

[mlubin]

Calling in @chriscoey

[mlubin]

I would vote for the "scaled" PSD cone to get the name PositiveSemidefiniteCone and the "unscaled" cone to get the longer name, like the LowerTrianglePositiveSemidefiniteCone, because it's really the lower triangle of entries in the cone. The scaled PSD cone makes much more sense to me and can be handled uniformly with other vector-based cones with regards to duality. The unscaled cone always needs to be a special case.

Edit: maybe VectorPositiveSemidefiniteCone and LowerTrianglePositiveSemidefiniteCone?

[blegat]

I like your idea. Why not TrianglePositiveSemidefiniteCone ? It does not matter whether it is upper or lower triangular.
In JuMP we will keep PSDCone for @constraint m X in PSDCone() and we will use TrianglePositiveSemidefiniteCone in conicdata ?

[mlubin]

So VectorPositiveSemidefiniteCone and TrianglePositiveSemidefiniteCone?

[mlubin]

@chriscoey and I have agreed on PositiveSemidefiniteConeScaled and PositiveSemidefiniteConeTriangle. What do you think?

[blegat]

I like the names ! I have updated the PR :)