Onn: convex discrete optimization

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Library card, focusing on circuits, Graver bases, and augmentation.

Shmuel Onn, "Convex discrete optimization," in Encyclopedia of Optimization (2009), 513--550.

Onn develops convex integer optimization through finite universal test sets, especially Graver bases. A Graver basis consists of conformally minimal integer kernel vectors; every integer dependence can be decomposed into such primitive sign-compatible moves (Lemma 4.2, p. 29). Circuits are the primitive integer kernel vectors of minimal support; every circuit lies in the Graver basis, the two sets coincide when the matrix is totally unimodular, and in general the Graver basis is much larger (p. 29).