Adapting step size algorithms for solving split equilibrium problems with applications to signal recovery

Abstract

Abstract Recent developments in split equilibrium problems (SEPs) have found practical applications in convex optimization problems, information theory, and signal processing. In this paper, we present three novel algorithms with no prior knowledge of the operator norm of a bounded linear operator to approximated solutions for SEPs. Strong convergence results are well presented under appropriate conditions. In addition, we illustrate our main results by providing various numerical examples. Their computational performances are compared with those previously studied in the literature, and the results are presented by showing numerical implementation of the sparse sensor signal recovery problem.

Keywords

• Fixed point problem
• Self-adaptive step size
• Equilibrium problem
• Signal recovery