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The following constrained matrix problem is studied. Find the matrix X that minimizes the Frobenius norm of $AX-B$, with A and B as given matrices and where X belongs to a closed convex cone. In particular we consider the cone of symmetric positive semidefinite (SPSD) matrices and the cone of (symmetric) elementwise nonnegative matrices. The optimal matrix is characterized, and the results are specialized to the two cases above. Further, we report from a numerical study of some projection-type algorithms.
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Andersson et al. (1997) studied this question.
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