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) : McCallum,Charles J. , Jr

Report Date : AUG 1970

Pagination or Media Count : 119

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 :   (*QUADRATIC PROGRAMMING, COMPLEX NUMBERS), (*LINEAR PROGRAMMING, COMPLEX NUMBERS), INVARIANCE, SET THEORY, MATRICES(MATHEMATICS), PARTIAL DIFFERENTIAL EQUATIONS, THEOREMS

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE