From Wikipedia, the free encyclopedia
Formulation in mathematical programming
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).
Definition
[edit]The mixed complementarity problem is defined by a mapping , lower values
and upper values
, with
.
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]References
[edit]- Stephen C. Billups (1995). "Algorithms for complementarity problems and generalized equations" (PS). Retrieved 2006-08-14.
- Francisco Facchinei, Jong-Shi Pang (2003). Finite-Dimensional Variational Inequalities and Complementarity Problems, Volume I.
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