Abstract: In this paper, a relaxed parallel $\varepsilon$-subgradient projection algorithm which includes the over-relaxed case  and an accelerated parallel $\varepsilon$-subgradient projection algorithm  for solving convex feasibility problem (CFP) are presented. Compared with the previous subgradient projection algorithms, the algorithms presented in this paper use parallel process, i.e. in each iteration consider several approximation subgradient projections simultaneously.  Algorithms adopt over-relaxed iterative process and accelerated technique. Hence, they can reduce the amounts of data storage and   improve the convergence speed.  And we also discuss the convergence of the methods under some mild conditions. Finally, the results of numerical experiment indicate that the  algorithms are valid and have faster convergence speed than that of the algorithm in [18].

Key words: convex feasibility problem, approximation subgradient, convergence analysis