Chapter

Convex Programming

S. N. Afriat

in Logic of Choice and Economic Theory

Published in print November 1987 | ISBN: 9780198284611
Published online November 2003 | e-ISBN: 9780191595844 | DOI: http://dx.doi.org/10.1093/0198284616.003.0025
 Convex Programming

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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

Chapter.  5838 words. 

Subjects: Microeconomics

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