Lemke's algorithm
Encyclopedia
In mathematical optimization, Lemke's algorithm is an procedure
for solving linear complementarity problem
s, and more generally mixed linear complementarity problem
s.
Lemke's algorithm is of pivoting
or basis
-exchange type. Similar algorithms can compute Nash equilibria for two-person matrix and bimatrix games.
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
for solving linear complementarity problem
Linear complementarity problem
In mathematical optimization theory, the linear complementarity problem arises frequently in computational mechanics and encompasses the well-known quadratic programming as a special case...
s, and more generally mixed linear complementarity problem
Mixed linear complementarity problem
In mathematical optimization theory, the mixed linear complementarity problem, often abbreviated as MLCP or LMCP, is a generalization of the linear complementarity problem to include free variables.- References :*...
s.
Lemke's algorithm is of pivoting
Pivot element
The pivot or pivot element is the element of a matrix, an array, or some other kind of finite set, which is selected first by an algorithm , to do certain calculations...
or basis
Matroid
In combinatorics, a branch of mathematics, a matroid or independence structure is a structure that captures the essence of a notion of "independence" that generalizes linear independence in vector spaces....
-exchange type. Similar algorithms can compute Nash equilibria for two-person matrix and bimatrix games.