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Lagrange Multipliers Revisited

In: Traces and Emergence of Nonlinear Programming

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  • Morton Slater

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 $$ \leq g; \; for \; \underline{all} \;x \geq 0 ?$$

Suggested Citation

  • Morton Slater, 2014. "Lagrange Multipliers Revisited," Springer Books, in: Giorgio Giorgi & Tinne Hoff Kjeldsen (ed.), Traces and Emergence of Nonlinear Programming, edition 127, pages 293-306, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0439-4_14
    DOI: 10.1007/978-3-0348-0439-4_14
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