  Hyperbolic programming is the problem of computing the infimum of a linear
function when restricted to the hyperbolicity cone of a hyperbolic polynomial,
a generalization of semidefinite programming. We propose an approach based on
symbolic computation, relying on the multiplicity structure of the algebraic
boundary of the cone, without the assumption of determinantal representability.
This allows us to design exact algorithms able to certify the multiplicity of
the solution and the optimal value of the linear function.
