# Accession Number:

## AD0712769

# Title:

## THE LINER COMPLEMENTARITY PROBLEM IN COMPLEX SPACE.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## STANFORD UNIV CALIF OPERATIONS RESEARCH HOUSE

# Personal Author(s):

# Report Date:

## 1970-08-01

# Pagination or Media Count:

## 119.0

# Abstract:

Duality theorems for linear and quadratic programming have recently been extended to complex space by Levinson and by Hanson and Mond. In real space, linear and convex quadratic programs can be unified by the Linear Complementarity Problem LCP for which pivoting algorithms are available. In this paper, a similar result is sought for complex space. The Complex LCP is formulated and then investigated from both existential and constructive points of view. The duality results of complex linear and quadratic programming are reviewed and the Complex LCP that is formulated is shown to give complex linear and quadratic programs as special cases. An existence theory is developed by means of complex versions of an alternative theorem, the Frank-Wolfe Theorem, and the Kuhn-Tucker Theorem. Various invariance theorems for principal pivoting in complex space are given. It is shown that the Complex LCP can not be solved by a natural pivoting algorithm in complex space however, a transformation of the problem enables one to solve it and hence complex linear and quadratic programs by means of real space pivoting theory. An example which utilizes this solution procedure is given in the Appendix. Author

# Descriptors:

# Subject Categories:

- Operations Research