Linear approximation method for solving split inverse problems and its applications

We study the problem of finding a common element that solves the multiple-sets feasibility and equilibrium problems in real Hilbert spaces. We consider a general setting in which the involved sets are represented as level sets of given convex functions, and propose a constructible linear approximation scheme that involves the subgradient of the associated convex functions. Strong convergence of the proposed scheme is established under mild assumptions and several synthetic and practical numerical illustrations demonstrate the validity and advantages of our method compared with related schemes in the literature.