The inertial relaxed algorithm with Armijo-type line search for solving multiple-sets split feasibility problem

Abstract

Abstract The multiple-sets split feasibility problem is the generalization of split feasibility problem, which has been widely used in fuzzy image reconstruction and sparse signal processing systems. In this paper, we present an inertial relaxed algorithm to solve the multiple-sets split feasibility problem by using an alternating inertial step. The advantage of this algorithm is that the choice of stepsize is determined by Armijo-type line search, which avoids calculating the norms of operators. The weak convergence of the sequence obtained by our algorithm is proved under mild conditions. In addition, the numerical experiments are given to verify the convergence and validity of the algorithm.

Keywords

• Multiple-sets split feasibility problem
• Inertia relaxed algorithm
• Armijo-type line search
• Convergence