 Mixed complementarity problem

Mixed Complementarity Problem (MCP) is a problem formulation in mathematical programming. Many wellknown problem types are special cases of, or may be reduced to MCP. It is a generalization of Nonlinear complementarity problem (NCP).
Definition
The mixed complementarity problem is defined by a mapping , lower values and upper values .
The solution of the MCP is a vector such that for each index one of the following alternatives holds:
 ;
 ;
 .
Another definition for MCP is: it is a variational inequality on the parallelepiped .
See also
References
 Stephen C. Billups (1995) (PS). Algorithms for complementarity problems and generalized equations. ftp://ftp.cs.wisc.edu/mathprog/techreports/9514.ps. Retrieved 20060814.
 Francisco Facchinei, JongShi Pang (2003). FiniteDimensional Variational Inequalities and Complementarity Problems, Volume I.
Complementarity problems and algorithms Complementarity Problems Basisexchange algorithms Simplex (Dantzig) · Crisscross · Lemke
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