In order to explore the minimum switching frequency required to regulate certain amount of harmonic components, a novel switching frequency minimized harmonic mitigation (SFMHM) model is proposed in this paper, which can regulate <inline-formula><tex-math notation="LaTeX"> \mathit{N}\mathbf{-1}</tex-math></inline-formula> harmonics with far less than N switching angles. By flexibly adjusting the threshold values, the proposed model can achieve both harmonic elimination and mitigation objectives. Based on PWM discretization and supported by quadratic programming, the switching frequency in the proposed model is expressed as a quadratic objective function of the PWM waveform. The objectives as fundamental control and selected harmonic mitigations are realized by treating the numerical approximations of the Fourier coefficients as constraints, which are finally transformed into an optimization model with binary variables and can be easily solved by some optimization toolboxes such as YALMIP. Some computing results show that, compared with the conventional selective harmonic elimination/mitigation (SHE/SHM) methods, the number of switching angles required to mitigate the same number of harmonics under the proposed method has been significantly reduced. The switching frequency can be reduced a lot compared with the conventional SHE/SHM methods, e.g., by 40% for some modulation indexes. Simulations and experiments verify the correctness of proposed SFMHM model.