Algebraic Hilbert Field Characterizations of Asymptotic Duality States and Optimal Paths to Infinity.
CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP
Pagination or Media Count:
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
- Operations Research