CGS algorithms for constrained extremization of functions

CGS (conjugate Gram-Schmidt) algorithms are given for computing extreme points of a real-valued functionf(x) ofn real variables subject tom constraining equationsg(x)=0,M<n. The method of approach is to solve the system $$\begin{gathered} f'(x) + g'(x)*\lambda = 0 \hfill \\ g(x) = 0 \hfill \\ \end{gathered} $$ where λ is the Lagrange multiplier vector, by means of CGS algorithms for systems of nonlinear equations. Results of the algorithms applied to test problems are given, including several problems having inequality constraints treated by adjoining slack variables.