This paper considers the adaptive control of a class of nonlinear discrete time system with nonlinearly parametrized functions. In particular, the focus is on concave or convex parametrizations with unknown parameters. The solutions involved 2 tuning functions which are determined by a minmax optimization approach much like the continuous time counterparts found in the literature. Direct extension from continuous time case do not work very well due to the premature termination of the adaptive algorithm before zero tracking error can be achieved. In this paper, this problem is solved. The proposed algorithm can be shown to be stable and in some cases, achieve zero tracking error in steady state.