The algorithm of multiplier method is discussed from the view point of dual problem for nonlinear programming problem. We present a class of the updating algorithm of Lagrange multiplier which employs conjugate gradient method in order to accelerate the rate of convergence of multiplier method.
The rate of convergence of conjugate gradient multiplier method ranks next to that of quasi-Newton multiplier method. But, it is expected that the conjugate gradient multiplier method becomes a practical algorithm for nonlinear programming problems with many inequality constrains because there is no need of memory space to accumulate the information for Hessian inverse of dual objective function.