Lemke

Lemke is a surname of German origin that appears in various contexts beyond personal names. It is found in scholarly, scientific, and professional usage, often attracting attention because several algorithmic methods bear the name Lemke.

In mathematics and operations research, the name Lemke is associated with two notable algorithms. Lemke's algorithm is a pivot method for solving linear complementarity problems, a class of mathematical models that generalize linear programming and arise in optimization and economic applications. The algorithm works by following a path through the feasible region of a related reformulation to locate a solution under appropriate conditions.

Another prominent algorithm is the Lemke–Howson algorithm, named for Lemke and Howson, which computes Nash equilibria in two-player finite normal-form games. It uses a complementary pivot approach to trace a path along the players’ best-response polytopes to identify equilibrium points. The method is widely cited in game theory and is frequently implemented in computational economics and related fields.

As a surname, Lemke is borne by many individuals across different countries and disciplines, reflecting its Germanic roots. In reference works, the term Lemke often appears in discussions of linear complementarity, game theory, and related mathematical methods. See also entries on the Lemke–Howson algorithm and on Lemke’s algorithm for further detail on these specific methods.