Lemke's algorithm explained

In mathematical optimization, Lemke's algorithm is a procedure for solving linear complementarity problems, and more generally mixed linear complementarity problems. It is named after Carlton E. Lemke.

Lemke's algorithm is of pivoting or basis-exchange type. Similar algorithms can compute Nash equilibria for two-person matrix and bimatrix games.

References

• Book: Cottle. Richard W.. Pang. Jong-Shi. Stone. Richard E.. The linear complementarity problem . Computer Science and Scientific Computing. Academic Press, Inc.. Boston, MA. 1992. xxiv+762 pp. 0-12-192350-9 . 1150683.
• Book: Murty, K. G.. Linear complementarity, linear and nonlinear programming. Sigma Series in Applied Mathematics. 3. Heldermann Verlag. Berlin. 1988. xlviii+629 pp. 3-88538-403-5. dead. https://web.archive.org/web/20100401043940/http://ioe.engin.umich.edu/people/fac/books/murty/linear_complementarity_webbook/. 2010-04-01. (Available for download at the website of Professor Katta G. Murty.)

External links

• OMatrix manual on Lemke
• Chris Hecker's GDC presentation on MLCPs and Lemke
• Linear Complementarity and Mathematical (Non-linear) Programming
• Siconos/Numerics open-source GPL implementation in C of Lemke's algorithm and other methods to solve LCPs and MLCPs