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In this work, a formulation of alternating direction method of multipliers (ADMM) for addressing power amplifiers (PA) modeling and linearization problems is presented. The proposal consists on leveraging the implicit redundancy of the equations in order to achieve a distributed architecture. A detailed theoretical formulation of the method is provided in order to get a better comprehension of its advantages and the approach to integrating the technique in the standard direct learning architecture scheme for digital predistortion. In addition, a discussion on how the implicit regularization helps to deal with numerical problems is presented. It is proven that the implicit regression for the modeling and linearization of PAs can be carried out in a distributed fashion with similar accuracy, enabling the use of resource-constrained devices for digital predistortion. Furthermore, a computational assessment is presented for measuring in terms of arithmetic operations how simpler the devices that implement the proposed ADMM can be, compared with the classical least squares (LS) data-centralized approach. A proof of concept with three scenarios is included: the first two scenarios feature a commercial PA driven by 5G-NR signals with a bandwidth of 30 MHz, and the third scenario involves a commercial Doherty PA with a 100-MHz signal. In a first scenario, experimental results show that an ADMM implementation of a digital predistorter can achieve the same performance as the classical LS solution. The benefits of the proposed regularization are examined by assessing ADMM in a second scenario characterized by significant numerical instabilities. Finally, the robustness of the technique is illustrated through the linearization of the Doherty PA with a 100-MHz OFDM signal.