  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.
