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In this paper, we consider the multiple-sets split feasibility problem in real Hilbert space and propose a self-adaptive method that uses projections onto quadratic (balls) approximations of the problem's associated sets. Our algorithm has several major advantages over existing methods in the literature. The first is its simple implementation as it uses closed-formula projection onto balls, and the second is that strong convergence is obtained under mild conditions. Several numerical experiments illustrate and compare the performances of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we examine how can one achieve equilibrium when two related non-cooperative strategic games are being played. We propose a split generalized Nash equilibrium problem for two non-cooperative strategic games and also define an equivalent split quasi-variational inequality problem. Further, by using the techniques of proving existence of quasi-variational inequality problems, we establish the existence of equilibria. Moreover, as an application, we investigate our split generalized Nash equilibrium problem in the terms of river basin pollution problem. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of bilevel multiple-sets split pseudomonotone equilibrium problems in real Hilbert spaces. A new parallel projection method is presented and a strong convergence theorem for solving the problem is established under mild assumptions. Our result is general and extends several existing results in the literature. [ABSTRACT FROM AUTHOR]

Inverse problems are characterized by their inherent non-uniqueness and sensitivity with respect to data perturbations. Their stable solution requires the application of regularization methods including variational and iterative regularization methods. Superiorization is a heuristic approach that can steer basic iterative algorithms to have small value of a certain regularization functional while keeping the algorithms simplicity and computational efforts, and is able to account for additional prior information. In this note, we combine the superiorization methodology with iterative regularization and show that the superiorized version of the scheme yields again a regularization method, however accounting for different prior information. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the problem of finding minimum-norm solutions of a split convex feasibility problem in real Hilbert spaces. We study and analyze the convergence of a new self-adaptive CQ algorithm. The main advantage of the algorithm is that there is no need to calculate the norm of the involved operator. [ABSTRACT FROM AUTHOR]