Criss-cross methods: A fresh view on pivot algorithms

@article{Fukuda1997CrisscrossMA,
  title={Criss-cross methods: A fresh view on pivot algorithms},
  author={K. Fukuda and T. Terlaky},
  journal={Mathematical Programming},
  year={1997},
  volume={79},
  pages={369-395}
}
Criss-cross methods are pivot algorithms that solve linear programming problems in one phase starting with any basic solution. The first finite criss-cross method was invented by Chang, Terlaky and Wang independently. Unlike the simplex method that follows a monotonic edge path on the feasible region, the trace of a criss-cross method is neither monotonic (with respect to the objective function) nor feasibility preserving. The main purpose of this paper is to present mathematical ideas and… Expand
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  • S. Zhang
  • Mathematics, Computer Science
  • Eur. J. Oper. Res.
  • 1999
  • 21
  • PDF
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  • 11
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...
1
2
3
4
5
...

References

SHOWING 1-10 OF 140 REFERENCES
New variants of finite criss-cross pivot algorithms for linear programming
  • S. Zhang
  • Mathematics, Computer Science
  • Eur. J. Oper. Res.
  • 1999
  • 21
  • PDF
A convergent criss-cross method
  • 94
Notes on Bland’s pivoting rule
  • 111
  • PDF
Pivot rules for linear programming: A survey on recent theoretical developments
  • 125
  • PDF
An exponential example for Terlaky's pivoting rule for the criss-cross simplex method
  • Kees Roos
  • Mathematics, Computer Science
  • Math. Program.
  • 1990
  • 46
...
1
2
3
4
5
...