Numerical Search and Equilibrium Methods

Numerical methods that search a space of candidate points or strategies for an optimum or an equilibrium by moving from one candidate to the next. The Nelder-Mead method, also called the downhill simplex method, finds a local minimum or maximum of a function by comparing function values alone and is often applied to nonlinear problems for which derivatives may not be known, and the Lemke-Howson algorithm, named after Carlton E. Lemke and J. T. Howson, computes a Nash equilibrium of a two-player game given as a pair of payoff matrices. An algorithm belongs here when its cited article describes a numerical search method for an optimum or an equilibrium that does not rely on gradients. It excludes methods that use gradients, which belong with the gradient and quasi-Newton methods, and algorithms that solve linear programs, which have their own group.