Bound-constrained polynomial optimization using only elementary calculations

We provide a monotone nonincreasing sequence of upper bounds f H k (k≥1) fkH(k≥1) converging to the global minimum of a polynomial <i>f</i> on simple sets like the unit hypercube in ℝ^<i>n</i>. The novelty with respect to the converging sequence of upper bounds in Lasserre [Lasserre JB (2010) A new look at nonnegativity on closed...

Moment methods in extremal geometry

In this thesis we develop techniques for solving problems in extremal geometry. We give an infinite dimensional generalization of moment techniques from polynomial optimization. We use this to construct semidefinite programming hierarchies for approximating optimal packing densities and ground state energies of particle systems. For this we...