The goal of this Note is to prove results in optimization of two integer variables which correspond to fundamental results in convex analysis of real variables, viz. that a local minimum of a convex function is global; that the marginal function of a convex function is convex; and that two disjoint convex sets can be separated by a hyperplane.

Received: 2007-06-28
Accepted: 2007-10-29
Published online: 2007-12-03
DOI: 10.1016/j.crma.2007.10.047

@article{CRMATH_2008__346_1-2_49_0,
     author = {Christer O. Kiselman},
     title = {Minima locaux, fonctions marginales et hyperplans s\'eparants dans l'optimisation discr\`ete},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {49--52},
     publisher = {Elsevier},
     volume = {346},
     number = {1-2},
     year = {2008},
     doi = {10.1016/j.crma.2007.10.047},
     language = {fr},
}

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Christer O. Kiselman. Minima locaux, fonctions marginales et hyperplans séparants dans l'optimisation discrète. Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 49-52. doi : 10.1016/j.crma.2007.10.047. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.10.047/