Mixed-numerology transmission is proposed to support a variety of communication scenarios with diverse requirements. However, as the orthogonal frequency division multiplexing (OFDM) remains as the basic waveform, the peak-to average power ratio (PAPR) problem is still cumbersome. In this paper, based on the iterative clipping and filtering (ICF) and optimization methods, we investigate the PAPR reduction in the mixed-numerology systems. We first illustrate that the direct extension of classical ICF brings about the accumulation of inter-numerology interference (INI) due to the repeated execution. By exploiting the clipping noise rather than the clipped signal, the noise-shaped ICF (NS-ICF) method is then proposed without increasing the INI. Next, we address the in-band distortion minimization problem subject to the PAPR constraint. By reformulation, the resulting model is separable in both the objective function and the constraints, and well suited for the alternating direction method of multipliers (ADMM) approach. The ADMM-based algorithms are then developed to split the original problem into several subproblems which can be easily solved with closed-form solutions. Furthermore, the applications of the proposed PAPR reduction methods combined with filtering and windowing techniques are also shown to be effective.