  Certificates of polynomial nonnegativity can be used to obtain tight dual
bounds for polynomial optimization problems. We consider Sums of Nonnegative
Circuit (SONC) polynomials certificates, which are well suited for sparse
problems since the computational cost depends only on the number of terms in
the polynomials and does not depend on the degrees of the polynomials. This
work is a first step to integrating SONC-based relaxations of polynomial
problems into a branch-and-bound algorithm. To this end, the SONC relaxation
for constrained optimization problems is extended in order to better utilize
variable bounds, since this property is key for the success of a relaxation in
the context of branch-and-bound. Computational experiments show that the
proposed extension is crucial for making the SONC relaxations applicable to
most constrained polynomial optimization problems and for integrating the two
approaches.
