On the relationship between a continuous update method of multipliers and the generalized reduced gradient method

Abstract The method of multipliers 1–3 (MOM) is a transformation technique which has enjoyed considerable popularity in recent years. The algorithmic philosophy is similar to conventional penalty function methods in that a constrained nonlinear programming problem is transformed into a sequence of unconstrained problems. In the standard MOM approach, the multipliers are updated after each unconstrained search. In this paper we investigate methods which involve continuous updating of the penalty parameters and design variables. We demonstrate that this continuous updating scheme is equivalent to the generalized reduced gradient method 4,5 applied to a certain dual problem. Computational results are given which suggest that the continuous updating MOM is not as efficient as one might reasonably hope.