Algebraic duality theorems for infinite LP problems

Pintér, Miklós (2011) Algebraic duality theorems for infinite LP problems. Linear algebra and its applications, 434 (3). pp. 688-693. DOI 10.1016/j.laa.2010.09.007

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Official URL: http://www.sciencedirect.com/science/article/pii/S0024379510004702

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.

Item Type:

Article

Uncontrolled Keywords:

infinite dimensional duality theorems, TU games with infinitely many players, Core, Bondareva-Shapley theorem, Exact games

Divisions:

Faculty of Economics > Department of Mathematics

Subjects:

Mathematics, Econometrics

Funders:

János Bolyai Research Scholarship of the Hungarian Academy of Sciences

Projects:

OTKA