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An iterative approach to quadratic optimization. (English) Zbl 1043.90063
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.

90C20Quadratic programming
90C48Programming in abstract spaces
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