Projection algorithms with dynamic stepsize for constrained composite minimization

Abstract

The problem of minimizing the sum of a large number of component functions over the intersection of a finite family of closed convex subsets of a Hilbert space is researched in the present paper. In the case of the number of the component functions is huge, the incremental projection methods are frequently used. Recently, we have proposed a new incremental gradient projection algorithm for this optimization problem. The new algorithm is parameterized by a single nonnegative constant μ. And the algorithm is proved to converge to an optimal solution if the dimensional of the Hilbert space is finite the step size is diminishing (such as αn = O(1/n)). In this paper, the algorithm is modified by employing the constant and the dynamic stepsize, and the corresponding convergence properties are analyzed.