Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these methods can outperform conventional optimization-based approaches in computational plasticity. However, in literature these algorithms are described individually for specific yield criteria, and hence there exists no guide for application of the algorithms to other yield criteria. This short paper presents a general form of algorithm design, independent of specific forms of yield criteria, that unifies the existing proximal gradient methods. Clear interpretation is also given to each step of the presented general algorithm so that each update rule is linked to the underlying physical laws in terms of mechanical quantities.