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A dual approach to linear inverse problems with convex constraints. (English) Zbl 0797.49019
The paper concerns the minimization of x under the constraints xK and Ax=β. Here K is a closed, convex subset of a Hilbert space S, A:SR N is linear, and βR N . A sufficient condition is given for the minimum solution to be x=P K A * (θ), where P K stands for the projection onto K and θR N . The condition is also necessary if βri(A(K)). A fixed point iteration is presented for computing the parameter θ.
MSC:
49K27Optimal control problems in abstract spaces (optimality conditions)
90C25Convex programming