Structures

opt,data = tssos_symmetry(pop, x, d, group; numeq=0, action=nothing, signsymmetry=false, semisimple=false, DiagSquare=false, SymmetricConstraint=true, TS="block", eqTS=TS, QUIET=false)

Compute the symmetry adapted moment-SOS relaxation for polynomial optimization problems. The model keyword accepts an empty JuMP GenericModel; both the SDP and the symmetry adapted basis use its numeric type. Use a fresh model per call.

Input arguments

• pop: polynomial optimization problem
• x: POP variables
• d: relaxation order
• group: permutation group acting on POP variables
• signsymmetry: true to detect common sign symmetries, or an n-by-k binary generator matrix (default false)
• semisimple: compute a semisimple representation instead of an irreducible representation
• numeq: number of equality constraints
• DiagSquare: include diagonal squares in the support (true, false)
• SymmetricConstraint: whether the constraints are symmetric or not
• TS: type of term sparsity ("block", "MD", "MF", false)
• eqTS: type of term sparsity for equality constraints (by default the same as TS, false)
• QUIET: run in the quiet mode (true, false)

Output arguments

• opt: optimum
• data: other auxiliary data