1. A method to control operation of a powertrain system including an internal combustion engine, a multi-mode transmission and a plurality of torque machines, said transmission configured to transfer torque among the engine, the torque machines, and an output member, the method comprising: establishing an objective component equation corresponding to an object component of interest; imposing, by a controller, a plurality of linear constraints and a non-linear constraint on the objective component equation; solving the objective component equation in relation to the plurality of the linear constraints and the non-linear constraint to determine extrema for the object component of interest; and employing said extrema to control operation of the powertrain system.