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We present a semidefinite programming (SDP) approach for the problem of ordering vertices of a layered graph such that the edges of the graph are drawn as vertical as possible. This Multi-Level Vertical Ordering (MLVO) problem is a quadratic ordering problem and conceptually related to the well-studied problem of Multi-Level Crossing Minimization (MLCM). In contrast to the latter, it can be formulated such that it does not merely consist of multiple sequentially linked bilevel quadraticdoi:10.1287/ijoc.1120.0525 fatcat:qztfqr2mfve2jkg3h27sjt2kki