1. A method for operating a powertrain system including a multi-mode transmission configured to transfer torque among an engine, torque machines, and a driveline, the method comprising: determining an objective function for an object component of interest; determining constraints for a plurality of independent variables and dependent variables; evaluating a plurality of permutations of the objective function with reference to the independent variables and the dependent variables; evaluating the objective function to determine maximum and minimum values for the objective function for each of the permutations; determining overall minimum and maximum values for the objective function based upon the maximum and minimum values for the objective function for each of the permutations; and controlling operation of the powertrain system associated with the object component of interest based upon the overall minimum and maximum values for the objective function.