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An iterative approach to quadratic optimization. (English) Zbl 1043.90063
Summary: Assume that C 1 ,,C N are N closed convex subsets of a real Hilbert space H having a nonempty intersection C. Assume also that each C i is the fixed point set of a nonexpansive mapping T i of H. We devise an iterative algorithm which generates a sequence (x n ) from an arbitrary initial x 0 H. The sequence (x n ) is shown to converge in norm to the unique solution of the quadratic minimization problem min xC (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.

MSC:
90C20Quadratic programming
90C48Programming in abstract spaces