43 citations · 135 across the 14 of their papers we have counts for
7 papers · 1 filter
Solving clustered low-rank semidefinite programs arising from polynomial optimization
Nando Leijenhorst, David de Laat
We study a primal-dual interior point method specialized to clustered low-rank semidefinite programs requiring high precision numerics, which arise from certain multivariate polyno…
-point semidefinite programming bounds for equiangular lines
David de Laat, Fabrício Caluza Machado, Fernando Mário de Oliveira Filho +1
We give a hierarchy of -point bounds extending the Delsarte-Goethals-Seidel linear programming -point bound and the Bachoc-Vallentin semidefinite programming -point bound…
Lower bounds on matrix factorization ranks via noncommutative polynomial optimization
Sander Gribling, David de Laat, Monique Laurent
We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particul…
Moment methods in energy minimization: New bounds for Riesz minimal energy problems
David de Laat
We use moment techniques to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate (from b…
Matrices with high completely positive semidefinite rank
Sander Gribling, David de Laat, Monique Laurent
A real symmetric matrix is completely positive semidefinite if it admits a Gram representation by (Hermitian) positive semidefinite matrices of any size . The smallest such…
A semidefinite programming hierarchy for packing problems in discrete geometry
David de Laat, Frank Vallentin
Packing problems in discrete geometry can be modeled as finding independent sets in infinite graphs where one is interested in independent sets which are as large as possible. For…
Fourier analysis on finite groups and the Lovász theta-number of Cayley graphs
Evan DeCorte, David de Laat, Frank Vallentin
We apply Fourier analysis on finite groups to obtain simplified formulations for the Lovász theta-number of a Cayley graph. We put these formulations to use by checking a few cases…