Reduction of Constrained Maxima to Saddle point Problems

Abstract

The usual applications of the method of Lagrangian multipliers, used in locatingconstrained extrema (say maxima), involve the setting up of the Lagrangian expression,(1) phi +(x, y) =f(x) +y'g(x),where f(x) is being (say) maximized with respect to the (vector) variable x = x,XNJ, subject to the constraint g(x) = 0, where g(x) maps the points of the N-dimensionalx-space into an M-dimensional space, and y = Iyi,.-. , YM} is the Lagrange multiplier(vector). Here, { I indicates a column vector; the prime indicates transposition, sothat y' is a row vector.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1956
Accession Number
AD1028600

Entities

People

  • Kenneth J. Arrow
  • Leonid Hurwicz

Organizations

  • Stanford University

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  • Materials and Manufacturing Processes

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  • Air Force
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  • Inequalities
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Fields of Study

  • Mathematics

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  • Approximation Theory.
  • Linear Algebra

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