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In visible light communication (VLC), the data is transmitted by modulating the light emitting diode (LED). The data-rate is throttled by the narrow modulation bandwidth of LEDs, which becomes a barrier for attaining high transmission rates. Non-orthogonal multiple access (NOMA) is a new scheme envisioned to improve the system capacity. In addition to multiple access schemes, optimization techniques are applied to further improve the data rate. In this letter, convex optimization is applied to NOMA-based VLC system for downlink. The proposed optimization system is analyzed in terms of the bit error rate (BER) and the sum-rate.