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math.OC2022
The spectrum of the Grigoriev-Laurent pseudomoments
Dmitriy Kunisky, Cristopher Moore
Grigoriev (2001) and Laurent (2003) independently showed that the sum-of-squares hierarchy of semidefinite programs does not exactly represent the hypercube until deg…
math.OC2022
Dual bounds for the positive definite functions approach to mutually unbiased bases
Afonso S. Bandeira, Nikolaus Doppelbauer, Dmitriy Kunisky
A long-standing open problem asks if there can exist 7 mutually unbiased bases (MUBs) in , or, more generally, MUBs in for any that is not…
math.OC2018
A Gramian Description of the Degree 4 Generalized Elliptope
Afonso S. Bandeira, Dmitriy Kunisky
One of the most widely studied convex relaxations in combinatorial optimization is the relaxation of the cut polytope to the elliptope , which correspo…