# Accession Number:

## ADA083696

# Title:

## The Implicit Complementarity Problem: Part I.

# Descriptive Note:

## Management science research rept.,

# Corporate Author:

## CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP

# Personal Author(s):

# Report Date:

## 1980-04-01

# Pagination or Media Count:

## 32.0

# Abstract:

Given an n by n matrix A,n-vector b and a mapping m from R superscript n into R superscript n, the implicit complementary problem is to find a vector x in R superscript n so that Ax b or 0, X or mx and Ax b transposed x - mx 0. This is the first of two papers in which we study this complementarity problem via an implicitly defined mapping F which depends on a given splitting of the matrix A. In the present paper, we derive sufficient conditions for the problem to have a unique solution for each vector b and study the problem in connection with a least-element theory. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics