Several acceleration schemes for solving the multiple-sets split feasibility problem (Q445822)

Let \(N, M, t\) and \(r\) be positive integers, let \(\{C_i \mid C_i \subseteq \mathbb{R}^N,\, i =1,\dots,t\}\) and \(\{Q_j \mid Q_j \subseteq \mathbb{R}^M,\, j =1,\dots,r\}\) be two families of nonempty closed convex sets, and let \(A\) be a real \((M \times N)\)-matrix. The multiple-sets split feasibility problem (MSFP) consists in finding a point \(x^\ast \in \cap_{i=1}^tC_i\) such that \(Ax^\ast \in \cap_{j=1}^rC_j\).NEWLINENEWLINEThe authors develop a self-adaptive algorithm for the numerical solution of the (MSFP) and prove its convergence. A special case of this algorithm as well as an accelerating relaxed algorithm are investigated. Numerical experiments are also provided.