Criss-cross methods: A fresh view on pivot algorithms

1997/10/01 by Komei Fukuda, Tamás Terlaky · 25 citations
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Algorithm #Basis (linear algebra) #Combinatorics #Computer science #Function (biology) #Geometry #Iterative Methods for Nonlinear Equations #Linear programming #Mathematical optimization #Mathematics #Monotonic function #Path (computing) #Polynomial and algebraic computation #Simplex #Simplex algorithm #TRACE (psycholinguistics)

paper · open access · doi:10.1007/bf02614325

published in Mathematical Programming 79(1-3), 369-395 (Springer Science and Business Media LLC)

crossref issued 1997/10/01 · crossref published 1997/10/01 · crossref published-print 1997/10/01 · openalex publication_date 1997/10/01 · crossref created 2007/04/28 · crossref deposited 2019/05/20 · openalex created_date 2025/10/10 · crossref indexed 2026/02/13 · openalex updated_date 2026/07/23

Citations

• Sufficient matrices and the linear complementarity problem
• The linear complimentarity problem, sufficient matrices, and the criss-cross method
• A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
• Pivot rules for linear programming: A survey on recent theoretical developments
• On extremal behaviors of Murty's least index method
• Complementary pivot theory of mathematical programming
• Linear and quadratic programming in oriented matroids
• A quasi-polynomial bound for the diameter of graphs of polyhedra

Cited by

• Bland's rule [wikipedia]