Mixed complementarity problem

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Mixed Complementarity Problem (MCP) is a problem formulation in mathematical programming. Many well-known problem types are special cases of, or may be reduced to MCP. It is a generalization of nonlinear complementarity problem (NCP).


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[edit]


  • Stephen C. Billups (1995). "Algorithms for complementarity problems and generalized equations" (PS). Retrieved 2006-08-14. Cite journal requires |journal= (help)
  • Francisco Facchinei, Jong-Shi Pang (2003). Finite-Dimensional Variational Inequalities and Complementarity Problems, Volume I.