Improved Lower Bounds for Global Polynomial Optimisation

Abstract

We present a branch-and-bound algorithm to improve the lower bounds obtained by SONC/SAGE. The running time is fixed-parameter tractable in the number of variables. Furthermore, we describe a new heuristic to obtain a candidate for the global minimum of a multivariate polynomial, based on its SONC decomposition. Applying this approach to thousands of test cases, we mostly obtain small duality gaps. In particular, we optimally solve the global minimisation problem in about 70% of the investigated cases.