Mayday.jl is a naïve implementation of sums-of-squares (SoS) polynomial optimization through semidefinite programming (SDP), powered by JuMP and Julia.
SoS programming is used in control theory to search for controllers for a dynamical system (like a robot or airplane) and to find the set of states for which those controllers will be valid. To learn more about how SoS programming is used, check out http://underactuated.csail.mit.edu/underactuated.html?chapter=11
To use this package, you'll need an SDP solver with a JuMP interface. If you installed Mayday with Pkg.add(), then you've already gotten SCS.jl, a wrapper for the free SCS solver, and you're all set. You may also want to install Mosek, a proprietary solver, with Pkg.add("Mosek"). Mosek requires a license, but is free for academic use: https://mosek.com/introduction/buy-mosek and is generally faster.
Check out the examples folder for demonstrations.