In mathematical optimization, Lemke's algorithm is a procedure for solving

linear complementarity problem In mathematical optimization theory, the linear complementarity problem (LCP) arises frequently in computational mechanics and encompasses the well-known quadratic programming as a special case. It was proposed by Cottle and Dantzig in 1968. ...

s, and more generally mixed linear complementarity problems. It is named after Carlton E. Lemke. Lemke's algorithm is of pivoting or

basis Basis may refer to: Finance and accounting * Adjusted basis, the net cost of an asset after adjusting for various tax-related items *Basis point, 0.01%, often used in the context of interest rates * Basis trading, a trading strategy consisting ...

exchange Exchange may refer to: Physics *Gas exchange is the movement of oxygen and carbon dioxide molecules from a region of higher concentration to a region of lower concentration. Places United States * Exchange, Indiana, an unincorporated community * ...

type. Similar algorithms can compute

Nash equilibria In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equili ...

for two-person matrix and bimatrix games.

References

* * (Available for download at the website of Professo
Katta G. Murty
)

External links

Chris Hecker's GDC presentation on MLCPs and Lemke

Linear Complementarity and Mathematical (Non-linear) Programming
*

Siconos SICONOS is an Open Source scientific software primarily targeted at modeling and simulating non-smooth dynamical systems (NSDS): * Mechanical systems (Rigid body or solid) with Unilateral contact and Coulomb friction as we find in Non-smooth mec ...

/Numerics open-source GPL implementation in C of Lemke's algorithm and other methods to solve LCPs and MLCPs Optimization algorithms and methods {{algorithm-stub