An Iterative Approach to Quadratic Optimization |
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Authors: | Xu HK |
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Institution: | (1) Department of Mathematics, University of Durban-Westville, Durban, South Africa |
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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
0H. The sequence (xn) 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. |
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Keywords: | Iterative algorithms quadratic optimization nonexpansive mappings convex feasibility problems Hilbert spaces |
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