Jordan symmetry reduction for conic optimization over the doubly nonnegative cone: theory and software

A common computational approach for polynomial optimization problems (POPs) is to use (hierarchies of) semidefinite programming (SDP) relaxations. When the variables in POP are required be nonnegative – as case combinatorial problems, example these SDP typically involve matrices, i.e. they conic over doubly cone. The Jordan reduction, a symmetry reduction method optimization, was recently introduced symmetric cones by Parrilo and Permenter [Mathematical Programming 181(1), 2020]. We extend this cone, investigate its application known relaxations of quadratic assignment maximum stable set problems. also introduce new Julia software where implemented.