Assume that C1,...,CN are N closed convex subsets of a real Hilbert space H having a nonempty intersection C. Assume also that each Ci is the fixed point set of a nonexpansive mapping Ti of H. We devise an interative algorithm which generates a sequence (xn) from an arbitrary initial x0∈H. The sequence (xn) is shown to converge in norm to the unique solution of the quadratic minimization problem minx∈C((1/2)<Ax, x>-<x, u>), where A is a bounded linear strongly positive operator on H and u is a given point in H. Quadratic–quadratic minimization problems are also discussed.
