Iterative process for solving a multiple-set split feasibility problem

TL;DR: A nonconvex regularization of SFP is interested and three split algorithms for solving this general case are proposed, based on the DC (difference of convex) algorithm introduced by Pham Dinh Tao, the second one is nothing else than the celebrate forward-backward algorithm, and the third one uses a method introduced by Mine and Fukushima.

TL;DR: In this paper, a nonconvex regularization of SFP is proposed and three split algorithms for solving this general case are presented. But these algorithms are based on the DC (difference of convex) algorithm (DCA) introduced by Pham Dinh Tao, the second one in nothing else than the celebrate forward-backward algorithm and the third one using a method introduced by Mine and Fukushima.

TL;DR: In this article , a self-adaptive algorithm for solving the split common fixed point problem of quasi-pseudocontractive operators in Hilbert spaces is presented and strong convergence theorems are given under some mild assumptions.

TL;DR: A hybrid CQ projection algorithm with two projection steps and one Armijo-type line-search step for the split feasibility problem and preliminary numerical experiments show that the algorithm is efficient.

TL;DR: This book provides a largely self-contained account of the main results of convex analysis and optimization in Hilbert space, and a concise exposition of related constructive fixed point theory that allows for a wide range of algorithms to construct solutions to problems in optimization, equilibrium theory, monotone inclusions, variational inequalities, and convex feasibility.

TL;DR: A very broad and flexible framework is investigated which allows a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence in convex feasibility problems.

TL;DR: The Krasnoselskii?Mann (KM) approach to finding fixed points of nonlinear continuous operators on a Hilbert space was introduced in this article, where a wide variety of iterative procedures used in signal processing and image reconstruction and elsewhere are special cases of the KM iterative procedure.

TL;DR: Using an extension of Pierra's product space formalism, it is shown here that a multiprojection algorithm converges and is fully simultaneous, i.e., it uses in each iterative stepall sets of the convex feasibility problem.