Abstract
The algorithm of multiplier method is discussed from the view point of dual problem for nonlinear programming problem. We point out that if a sufficiently large penalty parameter is chosen, the updating algorithm of Lagrange multiplier will be similar to Newton's method for solving dual problem.
For the purpose of applying effectively this feature of updating algorithm and avoiding difficulty to minimize the multiplier function for a large penalty parameter, we propose a multiplier method employing information on condition number of Hessian matrix for its multiplier function. It is expected that the multiplier method employing information on condition number becomes a practical algorithm for nonlinear programming problems with many inequality constraints, because there is no need of memory space to store the information for Hessian inverse of dual objective function.
