This work is concerned with an abstract problem in the form of a variational inequality, or equivalently a minimization problem involving a non-differential functional. The problem is inspired by a formulation of the initial-boundary value problem of elastoplasticity. The objective of this work is to revisit the predictor-corrector algorithms that are commonly used in computational applications, and to establish conditions under which these are convergent or, at least, under which they lead to decreasing sequences of the functional for the problem. The focus is on the predictor step, given that the corrector step by definition leads to a decrease in the functional. The predictor step may be formulated as a minimization problem. Attention is given to the tangent predictor, a line search approach, the method of steepest descent, and a Newton-like method. These are all shown to lead to decreasing sequences.