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Zbl 0797.49019
Potter, Lee C.; Arun, K.S.
A dual approach to linear inverse problems with convex constraints.
(English)
[J] SIAM J. Control Optimization 31, No.4, 1080-1092 (1993). ISSN 0363-0129; ISSN 1095-7138/e

The paper concerns the minimization of $\Vert x\Vert$ under the constraints $x\in K$ and $Ax= \beta$. Here $K$ is a closed, convex subset of a Hilbert space $S$, $A: S\to R\sp N$ is linear, and $\beta\in R\sp N$. A sufficient condition is given for the minimum solution to be $x= P\sb K A\sp*(\theta)$, where $P\sb K$ stands for the projection onto $K$ and $\theta\in R\sp N$. The condition is also necessary if $\beta\in \text{ri}(A(K))$. A fixed point iteration is presented for computing the parameter $\theta$.
[C.Ursescu (Iaşi)]
MSC 2000:
*49K27 Optimal control problems in abstract spaces (nec./ suff.)
90C25 Convex programming

Keywords: fixed point iteration

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