Few-shot learning (FSL) enables adaptation to new tasks with only limited training data. In wireless communications, channel environments can vary drastically; therefore, FSL techniques can quickly adjust transceiver accordingly. In this paper, we develop two FSL frameworks that fit in wireless transceiver design. Both frameworks are base on optimization programs that can be solved by well-known algorithms like the inexact alternating direction method of multipliers (iADMM) and the inexact alternating direction method (iADM). As examples, we demonstrate how the proposed two FSL frameworks are used for the OFDM receiver and beamforming (BF) for the millimeter wave (mmWave) system. The numerical experiments confirm their desirable performance in both applications compared to other popular approaches, such as transfer learning (TL) and model-agnostic meta-learning.