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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Vydáno v:	Linear algebra and its applications Ročník 434; číslo 3; s. 688 - 693
Hlavní autor:	PINTER, Miklós
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier Inc 01.02.2011 Elsevier
Témata:	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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Abstract	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.
AbstractList	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.
Author	Pintér, Miklós
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Keywords	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
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SubjectTerms	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
Title	Algebraic duality theorems for infinite LP problems
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