Benoît Legat is a postdoc at MIT with Prof. Pablo Parrilo in the Laboratory for Information and Decision Systems (LIDS).
Depending on the applications, the requirement for a multivariate polynomial library may be efficient computation of product, division, substitution, evaluation, gcd or even Gröbner bases. It is well understood that the concrete representation to use for these polynomials depends on whether they are sparse or not. In this talk, we show that in Julia, the choice of representation also depends on whether to specialize the compilation on the variables.
Complex numbers appear in a variety of optimization problems such as AC optimal power flow problems (AC-OPF) and quantum information optimization. This talk presents the integration of complex numbers in JuMP. We first describe how to create complex variables and constraints with complex coefficients in JuMP. Then, we show how this addition makes use of the extensible design of MathOptInterface and JuMP. We illustrate this with examples from PowerModels.jl and SumOfSquares.jl.