Minimal Rank Completions for Overlapping Blocks

Published 21 Jun 2021 in math.OC, cs.NA, and math.NA | (2106.11267v1)

Abstract: We consider the multi-objective optimization problem of choosing the bottom left block-entry of a block lower triangular matrix to minimize the ranks of all block sub-matrices. We provide a proof that there exists a simultaneous rank-minimizer by constructing the complete set of all minimizers.

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