Abstract
This paper describes the theoretical and numerical aspects of the multiplier method in nonlinear programming problems. The theoretical results indicate that a local solution for the original problem and the corresponding Lagrange multipliers are found by solving the dual problem.
The convergence rate of the multiplier method is governed mainly by the iterative scheme of Lagrange multipliers for solving the dual problem. In this paper we present a class of the updating algorithm of Lagrange multipliers which employs quasi-Newton methods to accelerate convergence of the multiplier method.
Several different algorithmes are available as quasi-Newton methods. The quasi-Newton method that involves no accurate line search is applied in this paper, since this method requires fewer number of evaluating the dual function than other methods which make use of the accurate line search. Numerical results show that this algorithm is superior to the usual multiplier method.
