An Iterative Approach to Quadratic Optimization

H.K. Xu
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H.K. Xu: University of Durban-Westville

Journal of Optimization Theory and Applications, 2003, vol. 116, issue 3, No 9, 659-678

Abstract: Abstract 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 (xn) is shown to converge in norm to the unique solution of the quadratic minimization problem min x∈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.

Keywords: Iterative algorithms; quadratic optimization; nonexpansive mappings; convex feasibility problems; Hilbert spaces (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (26)

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DOI: 10.1023/A:1023073621589

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