A Gradient Method For Approximating Saddle Points and Constrained Maxima

Abstract

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