Speeding up the Reduced Gradient Method for Constrained Optimization

Abstract

In various technical applications the local minimum of a differentiable cost function must be found under constraints that are interpreted as embedded hypersurfaces in the whole space of search. Generally Lagrange's “Reduced Gradient Method” can be applied for solving such problems in which the Lagrange multipliers associated with the individual constraint equations have important physical interpretation, therefore it is desirable to compute them. Though in special cases this algorithm can be replaced by closed form calculations via considering the “Auxiliary Function”, in other cases the algorithmic realization cannot be avoided. In this paper it is shown that via avoiding the calculation of the individual Lagrange multipliers the algorithm can be made considerably faster especially if the constraint equations are appropriately handled. Simulation investigations are presented to substantiate the suggested method.