On the integrality gap of the maximum-cut semidefinite programming relaxation in fixed dimension

08/07/2018

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by   Fernando Mário de Oliveira Filho, et al.

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We describe a factor-revealing convex optimization problem for the integrality gap of the maximum-cut semidefinite programming relaxation: for each n ≥ 2 we present a convex optimization problem whose optimal value is the largest possible ratio between the value of an optimal rank-n solution to the relaxation and the value of an optimal cut. This problem is then used to compute lower bounds for the integrality gap.