This paper studies the optimal least squares (LS) and minimax design of hybrid filter bank analog to digital converters (HFB ADCs) using second order cone programming (SOCP). The resulting problem is convex and it allows linear and quadratic constraints such as prescribed signal reconstruction magnitude flatness and aliasing canceling error to be incorporated. Two new robust HFB ADC design algorithms based on stochastic uncertainty and worst-case uncertainty models are also proposed. Design results show that the SOCP approach offers more flexibility than conventional methods and the robust design algorithms are more robust to parameter uncertainties than the SOCP design when the uncertainties are not taken into account