Online efficiency optimization is an attractive option that can be easily integrated into motor drive software. Most of these online efficiency optimization methods reduce the flux in the machine, but flux reduction can have operational drawbacks. If a machine operates at a certain load with low flux when a load step-up occurs, the flux might not be sufficient to support the new load torque. Such a scenario could be common in dynamic load applications such hybrid and electric vehicles with abrupt braking and acceleration. An overload under flux weakening will cause the machine to stall. This paper investigates constrained loss minimization in induction machines. Results show that it is possible to update the flux optimization constraints to guarantee load support. They also show that shifting the power loss function dynamically can help this load support.