SumOfSquares.jl
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[WIP] Add support for exact newton polytope #2
Closes #2
- [ ] Multipartite
- [x] Exact Newton Polytope
- [ ] Tests
Note: motzkin polynomial is a nice test example
This would be a great feature showing off different Julia packages/interfaces working together. Also useful. For most polynomial problems that would be feasible to solve, the size wouldn't be too large for a good polyhedral computation package like CDDLib to handle, right?
Note that in YALMIP, this is done by default but it does not precompute the H-representation but rather get separating hyperplanes lazily by solving LP's in the V-representation. See section III.A of Pre- and Post-Processing Sum-of-Squares Programs in Practice.
We cannot really do this by default since it would require having an LP solver as a dependency but it would be nice to also have this feature. In the paper mentioned above the authors mention that there are sometimes issues with the H-representation methods.