ODE methods for optimization with equality constraints

In an optimization problem with equality constraints we define an accessory function that is similar but different from a normal penalty function. In the accessory function we demonstrate the need to use small values of the parameter associated with an equality constraint. Large values of the parameter create extraneous stationary points which destroy the global convergence properties of steepest descent methods. By using small values of the parameters in the accessory function, when the current point is far away from the solution and when the constraint violations are large we are led to a refined version of the established SUMT method.