Second and Higher Order Iteration in Lagrangian Method

Abstract

Multipliers plays an important role in penalty method. Present study deals with the second order multiplier iteration using Newtons method and their convergence in two variable. The facts about three variables is discussed in this paper with comparison which is outcome of the main result. In convex problem, the convergence is obtained, without using derivatives for rst order. For second order, convergence required second order derivative and can be guaranteed only for a smaller region of initial values of multipliers. Here the equation for third order Lagrangian multiplier is proposed and order of convergence is pending for future work. In the last section, geometrical interpretation is discussed.