Abstract
In this paper we consider how the choice of initical values of Lagrange multipliers and penalty parameter affects the convergence property of the multiplier method for solving constrained nonlinear programming problems.
We point out that if we choose a sufficiently large penalty parameter, the condition number of the principal Hessian matrix of the multiplier function will become clearly different depending on whether we choose the Lagrange multiplier to be larger or smaller than the optimal value σ*.
For the purpose of applying effectively this feature of multiplier function, we propose a multiplier method taking the condition number into account and choosing an initical value of the Lagrange multiplier to be sufficiently greater than σ*.
By a numerical example, we compare the convergence characteristics of the proposed multiplier method, in which we consider the condition number, with those of the usual multiplier method.
