Approximate subgradient projection algorithm for convex feasibility problem

Abstract

An ε-subgradient projection algorithm for solving a convex feasibility problem is presented. Based on the iterative projection methods and the notion of ε-subgradient, a series of special projection hyperplanes is established. Moreover, compared with the existing projection hyperplanes methods with subgradient, the proposed hyperplanes are interactive with ε, and their ranges are more larger. The convergence of the proposed algorithm is given under some mild conditions, and the validity of the algorithm is proved by the numerical test.