Optimisation problems involving polynomials arise in a wide variety of contexts, including operational research, statistics, probability, finance, computer science, structural engineering, statistical physics, combinatorial chemistry, computational biology and algorithmic graph theory. They are however extremely challenging to solve, both in theory and practice. Existing algorithms and software are capable of solving only very small instances to proven optimality, unless they have some amenable structure, such as sparsity or convexity.

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