An Iterative Approach to Quadratic Optimization



Assume that C1, . . . , 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 x0H. The sequence (xn) is shown to converge in norm to the unique solution of the quadratic minimization problem minxC(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.

Iterative algorithms quadratic optimization nonexpansive mappings convex feasibility problems Hilbert spaces 


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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • H.K. Xu
    • 1
  1. 1.Department of MathematicsUniversity of Durban-WestvilleDurbanSouth Africa

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