Mixed Complementarity Problem

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

The mixed complementarity problem is defined by a mapping $F(x): \mathbb^n \to \mathbb^n$, lower values $\ell_i \in \mathbb \cup \$ and upper values $u_i \in \mathbb\cup\$, with $i \in \$.

The solution of the MCP is a vector $x \in \mathbb^n$ such that for each index $i \in \$ one of the following alternatives holds:

* $x_i = \ell_i, \; F_i(x) \ge 0$;
* $\ell_i < x_i < u_i, \; F_i(x) = 0$;
* $x_i = u_i, \; F_i(x) \le 0$.

Another definition for MCP is: it is a variational inequality on the parallelepiped ell, u/math>.

See also

* Complementarity theory

References

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{{Mathematical programming

Mathematical optimization