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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1956
- Accession Number
- AD1028600
Entities
People
- Kenneth J. Arrow
- Leonid Hurwicz
Organizations
- Stanford University