Search

In this paper, we investigate the split equilibrium problems and fixed point problems in Hilbert spaces. We provide a unified framework for solving such problem in which the involved equilibrium bifunctions f and g are pseudomonotone and monotone, respectively, and the operators S and T are pseudocontractive. We suggest an iterative algorithm for solving the split problem and demonstrate its weak convergence. [ABSTRACT FROM AUTHOR]

In this paper, we consider the varying stepsize gradient projection algorithm (GPA) for solving the split equality problem (SEP) in Hilbert spaces, and study its linear convergence. In particular, we introduce a notion of bounded linear regularity property for the SEP, and use it to establish the linear convergence property for the varying stepsize GPA. We provide some mild sufficient conditions to ensure the bounded linear regularity property, and then conclude the linear convergence rate of the varying stepsize GPA. To the best of our knowledge, this is the first work to study the linear convergence for the SEP. [ABSTRACT FROM AUTHOR]

Split variational inclusion problem is an important problem, and it is a generalization of the split feasibility problem. In this paper, we present feasible algorithms for the split variational inclusion problems in Hilbert spaces, and provide convergence theorems for these algorithms. As application, we study the split feasibility problem in real Hilbert spaces. Final, numerical results are given for our main results. [ABSTRACT FROM AUTHOR]

We prove the solution existence and propose an iterative algorithm for solving equilibrium problems over the common solutions of a monotone equilibrium problem and the fixed points of a strictly pseudocontractive mapping in Hilbert spaces. The algorithm is a combination of the proximal point and Halpern methods. Strong convergence is established. [ABSTRACT FROM AUTHOR]

We discuss accelerated version of the alternating projection method which can be applied to solve the linear matrix inequality (LMI) problem. The alternating projection method is a well-known algorithm for the convex feasibility problem, and has many generalizations and extensions. Bauschke and Kruk proposed a reflection projection algorithm for computing a point in the intersection of an obtuse cone and a closed convex set. We carry on this research in two directions. First, we present an accelerated version of the reflection projection algorithm, and prove its weak convergence in a Hilbert space; second, we prove the finite termination of an algorithm which is based on the proposed algorithm and provide an explicit upper bound for the required number of iterations under certain assumptions. Numerical experiments for the LMI problem are provided to demonstrate the effectiveness and merits of the proposed algorithms. [ABSTRACT FROM AUTHOR]