A new convex reformulation and approximation hierarchy for polynomial optimisation
Seminar Room 1, Newton Institute
AbstractIn 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.
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