## Note on a Bard-type scheme for solving the complementarity problem

- K. G. Murty
- Opsearch 11 (1974) 123-130.
- 1974

@article{Rohn1990ASP, title={A Short Proof of Finiteness of Murty's Principal Pivoting Algorithm}, author={Jiri Rohn}, journal={Math. Program.}, year={1990}, volume={46}, pages={255-256} }

- Published 1990 in Math. Program.
DOI:10.1007/BF01585743

and introduce into basis the nonbasic variable in the pair Yk, zk, with pivot in the kth row. Murty showed in [2] that if M is a P-matrix, then the pivot choice is correct (the pivot is then nonzero due to Tucker 's result [4]) and proved that after a finite number of steps c7 becomes nonnegative and the algorithm terminates with a solution to (1)-(3). We shall reprove here the finiteness of his algorithm using this auxiliary result:

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