Originally posted by **tcunis** January 16, 2024
The interface for convex sum-of-squares problems (`sossol`) should support convex cones (e.g., Lorentz, SDP) for decision variables which are of degree zero.
We want to support the following cones:
1. Convex cones of scalars, vectors, and vectorized matrices in `casos.conic` and `casos.sdpsol`:
- `lin` (previously `l`): element-wise inequalities
- `lor`, `quad`, or `soc` (previously `q`): Lorentz (quadratic, second-order) cone
- `rot` (previously `r`): Rotated Lorentz cone
- `psd` (previously `s`): Cone of positive semi-definite matrices
- solver-specific cones, e.g., for MOSEK:
- `pow` : Power cone
- `exp` : Exponential cone
3. Derived cones of vectors and vectorized matrices in `casos.sdpsol`, in addition to those above:
- `dd` : Cone of diagonally-dominant matrices (relax to linear inequalities)
- `sdd` : Cone of scaled diagonally-dominant matrices (relax to second-order cone constraints)
- further derived cones, provided the conic solver supports the base cone; e.g., for MOSEK:
- `geo` : Geometric cone (relax to EXP)
4. Polynomial cones in `casos.sossol`:
- `lin` (previously `l`): coefficient-wise inequalities (reduces to element-wise inequalities for entries of degree zero)
- `sos` (previously `s`): cone of sum-of-squares polynomials (relax to PSD)
- `msos` : cone of matrix sum-of-squares polynomials (relax Kronecker product to PSD)
- `dsos` : cone of diagonally-dominant sum-of-squares polynomials (relax to DD)
- `sdsos` : cone of scaled diagonally-dominant sum-of-squares polynomials (relax to SDD)
- any of the cones above, provided the entries are of degree zero and cones are supported by the SDP solver
sdpsol
sossol
(and derived sum-of-squares solvers)Discussed in https://github.com/iFR-ACSO/casos/discussions/72