
Accession Number : AD0723094
Title : Algebraic Hilbert Field Characterizations of Asymptotic Duality States and Optimal Paths to Infinity.
Descriptive Note : Research rept.,
Corporate Author : CARNEGIEMELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP
Personal Author(s) : Jeroslow,R. G. ; Kortanek,K. O.
Report Date : AUG 1970
Pagination or Media Count : 36
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 R(M) 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 R((M) sup n). The authors give other results which relate R(M)  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 BenIsrael, Charnes, and Kortanek. (Author)
Descriptors : (*MATHEMATICAL PROGRAMMING, THEOREMS), HILBERT SPACE, CONVEX SETS, OPTIMIZATION, INEQUALITIES, TOPOLOGY, THEOREMS
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE