Add vector and matrix cones to sum-of-squares problems

[tcunis]

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

2. 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)

3. 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