Lagrange Multipliers Revisited

Morton Slater

A chapter in Traces and Emergence of Nonlinear Programming, 2014, pp 293-306 from Springer

Abstract: Abstract The present paper was inspired by the work of Kuhn and Tucker [1]. These authors transformed a certain class of constrained maximum problems into equivalent saddle value (minimax) problems. Their work seems to hinge on the consideration of still a third type of problem. A very simple but illustrative form of this problem is the following: let $$ x\;\epsilon $$ positive orthant of some finite dimensional Euclidean space, and let f and g be real valued functions of x with the property that whenever $$ f \geq 0, $$ then also $$ g \geq 0; $$ under what conditions can one then conclude that 3 a non-negative constant u such that uf $$ \leq g; \; for \; \underline{all} \;x \geq 0 ?$$

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0439-4_14

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DOI: 10.1007/978-3-0348-0439-4_14

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