Method and apparatus for controlling multi-mode powertrain system

A method for operating a powertrain system to transfer torque among an engine, torque machines, and a driveline includes executing a search to determine a preferred engine operating point for operating the powertrain system in a transmission range in response to an output torque request. The search includes employing a candidate torque normalization ratio to determine a candidate engine torque from a normalized torque search space, and determining a candidate power cost associated with operating the powertrain system at the candidate engine torque for each of a plurality of candidate engine speeds within an input speed range and a plurality of candidate torque normalization ratios. A preferred engine speed is determined, and includes the candidate engine speed corresponding to the one of the candidate engine torques associated with a minimum of the candidate power costs. Engine operation is controlled responsive to the preferred engine speed.