We did sorting-via-linear-programming as a simple exercise when I was studying maths in the mid 2000s. It was certainly not seen as a research grade problem.
In general if memory serves right, linear programming can solve every problem that's in P with some suitable linear time preprocessing. See https://en.wikipedia.org/wiki/P-complete for some background.
Inner point methods to solve linear programs should then give you the bridge to continuous domains.
In general if memory serves right, linear programming can solve every problem that's in P with some suitable linear time preprocessing. See https://en.wikipedia.org/wiki/P-complete for some background.
Inner point methods to solve linear programs should then give you the bridge to continuous domains.