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Zbl 1043.90063
Xu, H. K.
An iterative approach to quadratic optimization. (English)
[J] J. Optimization Theory Appl. 116, No. 3, 659-678 (2003). ISSN 0022-3239; ISSN 1573-2878/e

Summary: Assume that $C_{1}, \dots , C_{N}$ 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 $x_{0}{\in}H$. The sequence ($x_n$) is shown to converge in norm to the unique solution of the quadratic minimization problem $min_{x\in C}(1/2){\langle}Ax, x{\rangle}-{\langle}x, u{\rangle}$, 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 2000:: *90C20 Quadratic programming
90C48 Programming in abstract spaces

Keywords: Iterative algorithms; quadratic optimization; nonexpansive mappings; convex feasibility problems; Hilbert spaces

Cited in: Zbl 1165.47058

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Zentralblatt MATH Berlin [Germany]