Highly Influenced

# A Path-Following Projective Interior Point Method for Linear Programming

@article{Shaw1994APP, title={A Path-Following Projective Interior Point Method for Linear Programming}, author={Dong X. Shaw and Donald Goldfarb}, journal={SIAM Journal on Optimization}, year={1994}, volume={4}, pages={65-85} }

- Published 1994 in SIAM Journal on Optimization
DOI:10.1137/0804003

In this paper the authors present a projective interior point method which follows the "central trajectory" and finds an optimal solution in at most O(vL) iterations. This algorithm is essentially Anstreicher’s variant of Karmarkar’s projective algorithm with a weakened "ball update" for lower bounds. The result indicates that a strong relationship exists between projective and pathfollowing algorithms. The authors show that within a certain probabilistic framework the expected number of… CONTINUE READING