Non-monotonous sequential subgradient projection algorithm for convex feasibility problem

Abstract

The existing methods of projection for solving convex feasibility problem may lead to slow convergence when the sequences enter some narrow“corridor” between two or more convex sets. In this paper, we apply a technique that may interrupt the monotonity of the constructed sequence to the sequential subgradient projection algorithm to construct a non-monotonous sequential subgradient projection algorithm for solving convex feasibility problem, which can leave such corridor by taking a big step at different steps during the iteration. Under some suitable conditions, the convergence is proved.We also compare the numerical performance of the proposed algorithm with that of the monotonous algorithm by numerical experiments.