This paper presents a novel loss minimization technique for induction motor driven elevator systems (IMDES) to determine an energy optimum velocity pattern. The objective function consists of a differential equation relating total power losses in the induction motor to its rotor speed. The constraints are provided in terms of velocity and acceleration governed by passenger comfort. Since the velocity and acceleration are state variables, Pontryagin's minimum principle is used to determine the most optimum trajectory by forming an appropriate Hamiltonian function. Boundary conditions are specified and used to obtain the coefficients of the rotor speed equation. As the velocity is optimized, the total travel time is not fixed and treated as a variable. A fixed-point iterative procedure is used to estimate the travel time. Additional loss minimization is incorporated by optimizing the machine flux for the constrained portion of the velocity pattern. An algorithm for implementing the optimization scheme is explained in detail. The theoretical claims are supported with analytical and experimental results. Proposed technique is developed for IMDES, but it can be easily adapted to other drive applications as well.