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Certificates of polynomial nonnegativity can be used to obtain tight dualbounds for polynomial optimization problems. We consider Sums of NonnegativeCircuit (SONC) polynomials certificates, which are well suited for sparseproblems since the computational cost depends only on the number of terms inthe polynomials and does not depend on the degrees of the polynomials. Thiswork is a first step to integrating SONC-based relaxations of polynomialproblems into a branch-and-bound algorithm. To this end, the SONC relaxationfor constrained optimization problems is extended in order to better utilizevariable bounds, since this property is key for the success of a relaxation inthe context of branch-and-bound. Computational experiments show that theproposed extension is crucial for making the SONC relaxations applicable tomost constrained polynomial optimization problems and for integrating the twoapproaches.

Strengthening SONC Relaxations with Constraints Derived from Variable Bounds