An all-digital nonlinear transmit-side equalization technique based on Model Predictive Control (MPC) is presented. The MPC equalizer performs an online optimization subject to eye height constraints at the RX using transmit waveform as a variable. Compared to existing TX equalization schemes such as IIR or Tomlinson-Harashima Precoding, MPC has been shown to achieve the best eye performance for any type of channel, especially when the control signal resolution is low, with minimal overhead at the RX. A simplified Direct Search algorithm and architecture optimization techniques are proposed to realize the MPC equalizer for high-speed links. A 20-tap MPC transmitter has been implemented in 28nm FDSOI technology. For a multidrop channel, the equalizer achieves opening of a closed eye at 4.5Gb/s for PAM2 and 6Gb/s for PAM4 mode.