Local convergence of the diagonalized method of multipliers

In this study, we consider a modification of the method of multipliers of Hestenes and Powell in which the iteration is diagonalized, that is, only a fixed finite number of iterations of Newton's method are taken in the primal minimization stage. Conditions are obtained for quadratic convergence of the standard method, and it is shown that a diagonalization where two Newton steps are taken preserves the quadratic convergence for all multipler update formulas satisfying these conditions.This work constitutes part of the author's doctoral dissertation in the Department of Mathematical Sciences, Rice University, under the direction of Professor R. A. Tapia and was supported in part by ERDA Contract No. E-(40-1)-5046.The author would like to thank Professor Richard Tapia for his comments, suggestions, and discussions on this material.