Incremental gradient projection algorithm for constrained composite minimization problems

In this paper, we propose an incremental gradient projection algorithm for solving a minimization problem over the intersection of a finite family of closed convex subsets of a Hilbert space where the objective function is the sum of component functions. This algorithm is parameterized by a single nonnegative constant µ. If µ = 0, then the proposed algorithm reduces to the classical incremental gradient method. The weak convergence of the sequence generated by the proposed algorithm is studied if the step size is chosen appropriately. Furthermore, in the special case of constrained least squares problem, the sequence generated by the proposed algorithm is proved to be convergent strongly to a solution of the constrained least squares problem under less requirements for the step size.