mixed complementarity problem

The mixed complementarity problem is defined by a mapping $F(x):\; \backslash mathbb\{R\}^n\; \backslash to\; \backslash mathbb\{R\}^n$, lower values $\backslash ell\_i\; \backslash in\; \backslash mathbb\{R\}\; \backslash cup\; \backslash \{-\backslash infty\backslash \}$ and upper values $u\_i\; \backslash in\; \backslash mathbb\{R\}\backslash cup\backslash \{\backslash infty\backslash \}$, with $i\; \backslash in\; \backslash \{1,\; \backslash ldots,\; n\backslash \}$.

The solution of the MCP is a vector $x\; \backslash in\; \backslash mathbb\{R\}^n$ such that for each index $i\; \backslash in\; \backslash \{1,\; \backslash ldots,\; n\backslash \}$ one of the following alternatives holds:

• $x\_i\; =\; \backslash ell\_i,\; \backslash ;\; F\_i(x)\; \backslash ge\; 0$;
• ;
• $x\_i\; =\; u\_i,\; \backslash ;\; F\_i(x)\; \backslash le\; 0$.

Another definition for MCP is: it is a variational inequality on the parallelepiped $[\backslash ell,\; u]$.

• Complementarity theory

• {{cite web|author=Stephen C. Billups|title=Algorithms for complementarity problems and generalized equations|date=1995| url=https://ftp.cs.wisc.edu/math-prog/tech-reports/95-14.ps|

format=PS|accessdate=2006-08-14}}

• {{cite book|author=Francisco Facchinei, Jong-Shi Pang|title=Finite-Dimensional Variational Inequalities and Complementarity Problems, Volume I|date=2003}}

{{Mathematical programming}}

Category:Mathematical optimization