The theory of and methods to solve complementarity problems

In the complementarity problem a pair of points is found in an ?z-dimensional space that are related in a certain functional way and whose coordinates are nonnegative while in each pair of associated coordinates a maximum of one quantity is nonzero. Theorems of existence and methods to solve linear and nonlinear complementarity problems and extensions to the case of infinitedimensional functional spaces are discussed. Such problems have numerous applications in mechanics, economics, and optimal control.