Reduction of Constrained Maxima to Saddle-Point Problems

Kenneth J. Arrow and Leonid Hurwicz

A chapter in Traces and Emergence of Nonlinear Programming, 2014, pp 61-80 from Springer

Abstract: Abstract The usual applications of the method of Lagrangian multipliers, used in locating constrained extrema (say maxima), involve the setting up of the Lagrangian expression, $$ \phi(x,y)=f(x)+y^{\prime}g(x), $$ where f(x) is being (say) maximized with respect to the (vector) variable x = {x1, • • •, xN}, subject to the constraint g(x)= O, where g(x) maps the points of the N-dimenaional x-space into an .M-dimensional space, and y ={y1, • • •, yM} is the Lagrange multiplier (vector).

Keywords: Local Maximum; Regularity Condition; Rand Corporation; BERKELEY Symposium; Left Member (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0439-4_3

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DOI: 10.1007/978-3-0348-0439-4_3

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