Non-orthogonal multiple access (NOMA) holds the promise to be a key enabler of 5G communication. However, the existing design of NOMA systems must be optimized to achieve maximum rate while using minimum transmit power. To do so, this paper provides a novel technique based on multi-objective optimization to efficiently allocate resources in the multi-user NOMA systems supporting downlink transmission. Specifically, our unique optimization technique jointly improves spectrum and energy efficiency while satisfying the constraints on users quality of services (QoS) requirements, transmit power budget and successive interference cancellation. We first formulate a joint problem for spectrum and energy optimization and then employ dual decomposition technique to obtain an efficient solution. For the sake of comparison, a low complexity single-objective NOMA optimization scheme is also provided as a benchmark scheme. The simulation results show that the proposed joint approach not only performs better than the traditional benchmark NOMA scheme but also significantly outperforms its counterpart orthogonal multiple access (OMA) schemes in terms of both energy and spectral efficiency.