Improving lifted dual solutions beyond the MRRW bound

Determine whether lifting a dual solution of the original Delsarte linear program to a higher level of the higher-order Delsarte hierarchies can be improved to yield an objective value surpassing the MRRW bound.

Background

The paper constructs explicit lifts of feasible dual solutions from lower levels to higher levels while preserving the appropriately scaled objective value. These lifted solutions provide a systematic way to transfer information from Delsarte’s original linear program to the higher-order hierarchy.

The authors leave unresolved whether the additional higher-level structure can be exploited by perturbing or otherwise improving a lifted solution so that its objective value gives a bound stronger than the classical MRRW bound.