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jump-dev / SumOfSquares.jl

Sum of Squares Programming for Julia
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quadratic coefficient of polynomial #260

Open YangBo17 opened 2 years ago

YangBo17 commented 2 years ago

The coefficient of polynomial can be quadratic，what is the theoretical basis?

blegat commented 2 years ago

What do you mean exactly by theoretical basis ? It happens often in control that you get quadratic expressions (or bilinear if you have no square). When you are looking for a quadratic polynomial, it gives a Bilinear Matrix Inequality (BMI). When you look for a polynomial of higher degree, you can reformulate it into a BMI using SumOfSquares.jl. The only solver in Julia that can solve BMI is https://jump.dev/JuMP.jl/stable/installation/#Supported-solvers at the moment. If you use DSOS you would get a QCQP though so it can be solved with Gurobi to global optimality or Ipopt to local optimality.