A Gradient Method For Approximating Saddle Points and Constrained Maxima

Kenneth J. Arrow and Leonid Hurwicz

A chapter in Traces and Emergence of Nonlinear Programming, 2014, pp 45-60 from Springer

Abstract: Abstract In the following, X and Y will be vectors with components Xi, Yj. By X ≥ 0 will be meant X ≥ 0 for all i. Let g(X), fj(X) (j=1, •••) be functions with suitable differentiability properties, where fj(X)≥0 for all X, and define $$ {\rm F}(\rm X, Y)=g(X)+{\sum_{j=1}^{m}} Y_{j}\Big\{1-[{f_{j}}(X)]^{l+\eta} \Big\}$$ .

Date: 2014
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DOI: 10.1007/978-3-0348-0439-4_2

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