A Revised Dual Projective Pivot Algorithm for Linear Programming

@article{Pan2005ARD,
  title={A Revised Dual Projective Pivot Algorithm for Linear Programming},
  author={Ping-Qi Pan},
  journal={SIAM Journal on Optimization},
  year={2005},
  volume={16},
  pages={49-68}
}
We revise the dual projective pivot algorithm using sparse rectangular LU factors. In each iteration, the proposed algorithm solves at most three triangular systems, while simplex algorithms solve four. Instead of the classical basis, it uses a so-called pseudobasis (a rectangular matrix having fewer columns than rows), thereby solving smaller linear systems with a potentially improved stability compared to simplex algorithms. Most importantly, it generates good search directions at a low cost… CONTINUE READING