Criss-cross methods: A fresh view on pivot algorithms

@article{Fukuda1997CrisscrossMA,
  title={Criss-cross methods: A fresh view on pivot algorithms},
  author={Komei Fukuda and Tam{\'a}s Terlaky},
  journal={Mathematical Programming},
  year={1997},
  volume={79},
  pages={369-395}
}
  • K. FukudaT. Terlaky
  • Published 1 October 1997
  • Economics, Computer Science
  • Mathematical Programming
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… 
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New variants of finite criss-cross pivot algorithms for linear programming

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