Symmetries in polynomial optimization

Abstract

This chapter investigates how symmetries can be used to reduce the computational complexity in polynomial optimization problems. A focus will be specifically given on the Moment-SOS hierarchy in polynomial optimization, where results from representation theory and invariant theory of groups can be used. In addition, symmetry reduction techniques which are more generally applicable are also presented.

This chapter will appear as part of a forthcoming book "Polynomial Optimisation, Moments, and Applications" presenting research acitivies conducted in the Marie Skłodowska-Curie Innovative Training Network POEMA