Algebraic duality theorems for infinite LP problems

In this paper, we consider a primal–dual infinite linear programming problem-pair, i.e. LPs on infinite dimensional spaces with infinitely many constraints. We present two duality theorems for the problem-pair: a weak and a strong duality theorem. We do not assume any topology on the vector spaces,...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 434; no. 3; pp. 688 - 693
Main Author: PINTER, Miklós
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 01.02.2011
Elsevier
Subjects:
Algebra
Bondareva–Shapley theorem
Core
Exact games
Exact sciences and technology
Infinite dimensional duality theorems
Linear and multilinear algebra, matrix theory
Mathematics
Sciences and techniques of general use
TU games with infinitely many players
TU games with infinitely many players
Bondareva–Shapley theorem
Infinite dimensional duality theorems
Exact games
Core
Vector space
Constraint
Primal dual method
Linear programming
Duality
Infinite dimension
Topology
Bondareva-Shapleytheorem
ISSN:0024-3795
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Summary:In this paper, we consider a primal–dual infinite linear programming problem-pair, i.e. LPs on infinite dimensional spaces with infinitely many constraints. We present two duality theorems for the problem-pair: a weak and a strong duality theorem. We do not assume any topology on the vector spaces, therefore our results are algebraic duality theorems. As an application, we consider transferable utility cooperative games with arbitrarily many players.
ISSN:0024-3795
DOI:10.1016/j.laa.2010.09.007