On the Slater condition for the SDP relaxations of nonconvex sets

We prove that all results determining the dimension and the affine hull of feasible solutions of any combinatorial optimization problem, and various more general nonconvex optimization problems, directly imply the existence of the Slater points for a very wide class of semidefinite programming relaxations of these nonconvex problems. Our proofs are very concise, constructive and elementary.

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