A new optimization-based iterative learning control algorithm is proposed and its properties derived. An important characteristic of this algorithm is that it uses present and future predicted errors to compute the current control, in a similar manner to model-based predictive control using a receding horizon. In particular, it enables the algorithm designer to achieve good control over convergence rate. The actual implementation has a multimodel structure but uses standard linear quadratic regulator methods for a causal formulation (in the iterative learning sense) of what is originally a non-causal algorithm. The results are illustrated by simulations.