# Accession Number:

## AD0723094

# Title:

## Algebraic Hilbert Field Characterizations of Asymptotic Duality States and Optimal Paths to Infinity.

# Descriptive Note:

## Research rept.,

# Corporate Author:

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

# Personal Author(s):

# Report Date:

## 1970-08-01

# Pagination or Media Count:

## 36.0

# Abstract:

Every finite subset of the following infinite set of inequalities has a solution, although there is no real solution to all these inequalities x or n, for n 0,1,2,3,... By the introduction of an infinitely large quantity M these inequalities obtain a solution x M in the field RM of the reals with M adjoined. It is shown that this solution is a special instance of the following general theorem every set of linear inequalities in R sup n whose every finite subset has a solution, itself has a solution RM sup n. The authors give other results which relate RM - solutions to asymptotic solutions in the reals, and use their main result to give an algebraic characterization of asymptotic duality states in a duality theory developed earlier by Ben-Israel, Charnes, and Kortanek. Author

# Descriptors:

# Subject Categories:

- Operations Research