A Splitting-relaxed Projection Method for Solving the Split Feasibility Problem
نویسنده
چکیده
The split feasibility problem (SFP) is to find x ∈ C so that Ax ∈ Q, where C is a nonempty closed convex subset of Rn, Q is a nonempty closed convex subset of Rm, and A is a matrix from Rn into Rm. One of successful methods for solving the SFP is Byrne’s CQ algorithm. However, to carry out the CQ algorithm, it is required that the closed convex subsets are simple and that the matrix norm is known in advance. Motivated by Tseng’s splitting method and Yang’s relaxed CQ algorithm, we propose in this paper a new method for solving the SFP, which overcomes the drawback of the CQ algorithm.
منابع مشابه
Extensions of the CQ Algorithm for the Split Feasibility and Split Equality Problems∗
The convex feasibility problem (CFP) is to find a member of the intersection of finitely many closed convex sets in Euclidean space. When the intersection is empty, one can minimize a proximity function to obtain an approximate solution to the problem. The split feasibility problem (SFP) and the split equality problem (SEP) are generalizations of the CFP. The approximate SFP (ASFP) and approxim...
متن کاملGraph Convergence for H(.,.)-co-Accretive Mapping with over-Relaxed Proximal Point Method for Solving a Generalized Variational Inclusion Problem
In this paper, we use the concept of graph convergence of H(.,.)-co-accretive mapping introduced by [R. Ahmad, M. Akram, M. Dilshad, Graph convergence for the H(.,.)-co-accretive mapping with an application, Bull. Malays. Math. Sci. Soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...
متن کاملSelf-Adaptive and Relaxed Self-Adaptive Projection Methods for Solving the Multiple-Set Split Feasibility Problem
and Applied Analysis 3 half-spaces, so that the algorithm is implementable. We need not estimate the Lipschitz constant and make a sufficient decrease of the objection function at each iteration; besides, these projection algorithms can reduce to the modifications of the CQ algorithm 6 when the MSSFP 1.1 is reduced to the SFP. We also show convergence the algorithms under mild conditions.
متن کاملConvergence of Weighted Averages of Relaxed Projections
The convergence of the algorithm for solving convex feasibility problem is studied by the method of sequential averaged and relaxed projections. Some results of H. H. Bauschke and J. M. Borwein are generalized by introducing new methods. Examples illustrating these generalizations are given.
متن کاملSimultaneous and semi-alternating projection algorithms for solving split equality problems
In this article, we first introduce two simultaneous projection algorithms for solving the split equality problem by using a new choice of the stepsize, and then propose two semi-alternating projection algorithms. The weak convergence of the proposed algorithms is analyzed under standard conditions. As applications, we extend the results to solve the split feasibility problem. Finally, a numeri...
متن کامل