Quadratic optimization of fixed points of nonexpansive mappings in Hilbert space

摘要: Finding an optimal point in the intersection of fixed sets a family nonexpansive mappings is frequent problem various areas mathematical science and engineering. Let be on Hilbert space H, let quadratic function defined by for all , where strongly positive bounded self-adjoint linear operator. Then, each sequence scalar parameters (λn) satisfying certain conditions, we propose algorithm that generates converting to unique minimizer u* Θ over Ti’s. This generalizes some results Halpern (1967), Lions (1977), Wittmann (1992), Bauschke (1996). In particular, minimization closed convex Ci can handled taking Ti metric projection onto without introducing any special inner products depends A. We also converging K...