EXTENSION OF DAVIDONS VARIABLE METRIC METHOD TO MAXIMIZATION UNDER LINEAR INEQUALITY AND EQUALITY CONSTRAINTS

Formulation of general problem to which the conjugate gradient method applies, notation is introduced, and the fundamental geometric concepts which underlie the method are presented. The basic algorithm is explained. Matrix representations for finite- dimensional projection operators and useful recursion relations are presented. The stability of the method is proved. Necessary and sufficient conditions for a point to be a global maximum are given. Method is them compared with other methods.