Mixed complementarity problem - Alchetron, the free social encyclopedia

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 ) : R n → R n , lower values ℓ i ∈ R ∪ { − ∞ } and upper values u i ∈ R ∪ { ∞ } .

The solution of the MCP is a vector x ∈ R n such that for each index i ∈ { 1 , … , n } one of the following alternatives holds:

x i = ℓ i , F i ( x ) ≥ 0 ;

ℓ i < x i < u i , F i ( x ) = 0 ;

x i = u i , F i ( x ) ≤ 0 .

Another definition for MCP is: it is a variational inequality on the parallelepiped [ ℓ , u ] .

References

Mixed complementarity problem Wikipedia

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