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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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Convex Programming

Convex Programming

(p.401) V.2 Convex Programming
Logic of Choice and Economic Theory

S. N. Afriat

Oxford University Press

This is the second of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making. It introduces convexity conditions, and shows where they have effect, together with Slater's condition, in assuring the existence of a support to the limit function, so providing Lagrange multipliers, or shadow prices, of resources that have part in the optimality conditions. Then for the case of differentiable functions the Kuhn–Tucker conditions are obtained. The six sections of the chapter are: convexity; programming convexity theorem; Slater's condition; optimality theorem; non‐negative maxima; the Kuhn–Tucker conditions.

Keywords:   choice, convex programming, convexity theorem, economic theory, Kuhn–Tucker conditions, Lagrange multipliers, limit function, mathematical economics, optimal programming, optimality theorem, shadow price, Slater's condition

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