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Logic of Choice and Economic Theory$
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S. N. Afriat

Print publication date: 1987

Print ISBN-13: 9780198284611

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198284616.001.0001

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Linear Programming

Linear Programming

Chapter:
(p.413) V.3 Linear Programming
Source:
Logic of Choice and Economic Theory
Author(s):

S. N. Afriat

Publisher:
Oxford University Press
DOI:10.1093/0198284616.003.0026

This is the third of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making. It discusses linear programming, which might appear to be a special case of convex programming, but is more substantial, and is really an embodiment of the theory of systems of linear inequalities (as reflected here). This chapter initiates the subject with reference to systems of linear inequalities and natural questions about them, and all LP (linear programming) theorems are encountered simply in pursuing those. Theorems about linear inequalities that have uses directly on their own are also derived (and are illustrated in many places in this book). The eight sections of the chapter are: linear inequalities; separation theorems; theorems of alternatives; polyhedra and polytopes; LP Duality Theorem; the pivot operation; the Simplex Algorithm; and BASIC program.

Keywords:   choice, duality, economic theory, linear inequalities, linear programming, LP Duality Theorem, mathematical economics, optimal programming, pivot operation, polyhedra, polytopes, separation theorems, Simplex Algorithm, theorems of alternatives

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