File tree Expand file tree Collapse file tree 1 file changed +2
-27
lines changed
src/Bridges/Constraint/bridges Expand file tree Collapse file tree 1 file changed +2
-27
lines changed Original file line number Diff line number Diff line change @@ -27,33 +27,8 @@ See also [`MOI.Bridges.Constraint.HermitianToSymmetricPSDBridge`](@ref).
2727
2828 * `F` in [`MOI.PositiveSemidefiniteConeTriangle`](@ref)
2929
30- ## Reformulation
31-
32- The reformulation is best described by example.
33-
34- The Hermitian matrix:
35- ```math
36- \\ begin{bmatrix}
37- x_{11} & x_{12} + y_{12}im & x_{13} + y_{13}im\\\\
38- x_{12} - y_{12}im & x_{22} & x_{23} + y_{23}im\\\\
39- x_{13} - y_{13}im & x_{23} - y_{23}im & x_{33}
40- \\ end{bmatrix}
41- ```
42- is positive semidefinite if and only if the symmetric matrix:
43- ```math
44- \\ begin{bmatrix}
45- x_{11} & x_{12} & x_{13} & 0 & y_{12} & y_{13} \\\\
46- & x_{22} & x_{23} & -y_{12} & 0 & y_{23} \\\\
47- & & x_{33} & -y_{13} & -y_{23} & 0 \\\\
48- & & & x_{11} & x_{12} & x_{13} \\\\
49- & & & & x_{22} & x_{23} \\\\
50- & & & & & x_{33}
51- \\ end{bmatrix}
52- ```
53- is positive semidefinite.
54-
55- The bridge achieves this reformulation by constraining the above matrix to
56- belong to the `MOI.PositiveSemidefiniteConeTriangle(6)`.
30+ Note that if `G` is `MOI.VectorAffineFunction{T}` then `F` will be
31+ `MOI.VectorAffineFunction{Complex{T}}`
5732"""
5833struct HermitianToComplexSymmetricBridge{T,F,G} <: SetMapBridge {
5934 T,
You can’t perform that action at this time.
0 commit comments