Lemke's algorithm
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
exchange type. Similar algorithms can compute Nash equilibria for two-person matrix and bimatrix games
.
References
- Cottle, Richard W.; Pang, Jong-Shi; Stone, Richard E. (1992). The linear complementarity problem. Computer Science and Scientific Computing. Boston, MA: Academic Press, Inc. pp. xxiv+762 pp. MR 1150683.
- Murty, K. G. (1988). Linear complementarity, linear and nonlinear programming. Sigma Series in Applied Mathematics. Vol. 3. Berlin: Heldermann Verlag. pp. xlviii+629 pp. MR949214
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