On an efficient implementation of the face algorithm for linear programming

Lei Hong Zhang*, Wei Hong Yang, Lizhi LIAO

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

6 Citations (Scopus)


In this paper, we consider the solution of the standard linear programming (LP). A remarkable result in LP claims that all optimal solutions form an optimal face of the underlying polyhedron. In practice, many real-world problems have infinitely many optimal solutions and pursuing the optimal face, not just an optimal vertex, is quite desirable. The face algorithm proposed by Pan [19] targets at the optimal face by iterating from face to face, along an orthogonal projection of the negative objective gradient onto a relevant null space. The algorithm exhibits a favorable numerical performance by comparing the simplex method. In this paper, we further investigate the face algorithm by proposing an improved implementation. In exact arithmetic computation, the new algorithm generates the same sequence as Pan's face algorithm, but uses less computational costs per iteration, and enjoys favorable properties for sparse problems.

Original languageEnglish
Pages (from-to)335-354
Number of pages20
JournalJournal of Computational Mathematics
Issue number4
Publication statusPublished - Jul 2013

Scopus Subject Areas

  • Computational Mathematics

User-Defined Keywords

  • Level face
  • Linear programming
  • Optimal face
  • Rank-one correction


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