TY - JOUR
T1 - On an Efficient Implementation of the Face Algorithm for Linear Programming
AU - Zhang , Leihong
AU - Yang , Weihong
AU - Liao , Lizhi
JO - Journal of Computational Mathematics
VL - 4
SP - 335
EP - 354
PY - 2013
DA - 2013/08
SN - 31
DO - http://doi.org/10.4208/jcm.1301-m4106
UR - https://global-sci.org/intro/article_detail/jcm/9739.html
KW - Linear programming, Level face, Optimal face, Rank-one correction.
AB - <p style="text-align: justify;">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&#39;s face algorithm, but uses less computational costs per iteration, and enjoys favorable properties for sparse problems.</p>