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A new convex reformulation and approximation hierarchy for polynomial optimisation

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If you have a question about this talk, please contact Mustapha Amrani.

Polynomial Optimisation

In this talk we will look at how any polynomial minimisation problem with a bounded feasible set can be reformulated into a conic maximisation problem with a single variable. By reformulated we mean that the optimal values of these problems are equal. The difficulty of the original problem goes into a cone of homogeneous polynomials which are nonnegative over a certain subset of the nonnegative orthant. We shall consider a new hierarchy of inner approximations to this cone. These approximations can be used to produce linear optimisation problems, whose optimal values provide a monotonically increasing sequence of lower bounds to the optimal value of the original problem. Using a new positivstellensatz, we shall show that this sequence of lower bounds in fact converges to the optimal value of the original problem.

This talk is part of the Isaac Newton Institute Seminar Series series.

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