Greedy systems of linear inequalities and lexicographically optimal solutions

• Fujishige, Satoru

  Research Institute for Mathematical Sciences, Kyoto University

Abstract

The present note reveals the role of the concept of greedy system of linear inequalities played in connection with lexicographically optimal solutions on convex polyhedra and discrete convexity. The lexicographically optimal solutions on convex polyhedra represented by a greedy system of linear inequalities can be obtained by a greedy procedure, a special form of which is the greedy algorithm of J. Edmonds for polymatroids. We also examine when the lexicographically optimal solutions become integral. By means of the Fourier–Motzkin elimination Murota and Tamura have recently shown the existence of integral points in a polyhedron arising as a subdifferential of an integer-valued, integrally convex function due to Favati and Tardella [Murota and Tamura, Integrality of subgradients and biconjugates of integrally convex functions. Preprint arXiv:1806.00992v1 (2018)], which can be explained by our present result. A characterization of integrally convex functions is also given.

Journal

• RAIRO - Operations Research

  RAIRO - Operations Research 53 (5), 1929-1935, 2019-11

  EDP Sciences

Keywords

• Greedy system
• lexicographic optimality
• discrete convexity
• integrally convex functions

Details

• CRID: 1050845763870238848
• NII Article ID: 120006770227
• ISSN: 03990559
• ISSN: 12903868
• DOI: 10.1051/ro/2019001
• HANDLE: 2433/244873
• Web Site: https://www.rairo-ro.org/10.1051/ro/2019001/pdf
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN