In-band, full-duplex (IBFD) radio frequency (RF) users generate self-interference that obstructs receiver operations. This interference may be mitigated using several techniques, including antenna isolation, circulators, digital mitigation, and analog mitigation at the carrier frequency. We apply an analog mitigation technique that uses a sparse tap-delay model to reduce power and computational complexity. We demonstrate that optimizing the weights of the resulting equalizer achieves sufficient self-interference mitigation, even under realistic hardware limitations. The performance is limited by i) how many delay taps are chosen, ii) how closely this discrete model matches the actual channel, iii) the dynamic range of the weighting coefficients, and iv) the timing precision of the system. We compare the achievable performance of this technique under different combinations of these limitations. We propose a sparse, constrained optimization solution that offers sufficient self-interference mitigation and significantly reduces the power consumption.