Inertial accelerated algorithms for solving a split feasibility problem

Inspired by the inertial proximal algorithms for finding a zero of a maximal monotone operator, in this paper, we propose two inertial accel erated algorithms to solve the split feasibility problem. One is an inertial relaxed-CQ algorithm constructed by applying inertial technique to a relaxed- CQ algorithm, the other is a modified inertial relaxed-CQ algorithm which combines the KM method with the inertial relaxed-CQ algorithm. We prove their asymptotical convergence under some suitable conditions. Numerical re sults are reported to show the effectiveness of the proposed algorithms

Convergence analysis of a parallel projection algorithm for solving convex feasibility problems

The convex feasibility problem (CFP) is a classical problem in nonlinear analysis. In this paper, we propose an inertial parallel projection algorithm for solving CFP. Different from the previous algorithms, the proposed method introduces a sequence of parameters and uses the information of last two iterations at each step. To prove its convergence in a simple way, we transform the parallel algorithm to a sequential one in a constructed product space. Preliminary experiments are conducted to demonstrate that the proposed approach converges faster than the general extrapolated algorithms