Holographic complexity for nonlinearly charged Lifshitz black holes

Using "complexity=action" proposal we study the late time growth rate of holographic complexity for nonlinear charged Lifshitz black hole with a single horizon or two horizons. As a toy model, we consider two kinds of such black holes: nonlinear charged Lifshitz black hole and nonlinear logarithmic charged Lifshitz black hole. We find that for the black hole with two horizons, the action growth bound is satisfied. But for the black hole with a single horizon, whether the Lloyd bound is violated depends on the specific value of dimensionless coupling constants $\beta_{1},\beta_{2}$, spacetime dimension $D$ and dynamical exponent $z$.