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.

翻译：我们认为,选择一个区块下三角三角矩阵的左下方块块进入以尽量减少所有区块次矩阵的排名,是一个多目标优化问题。 我们通过构建全部最小化器集来证明同时存在一个级最小化器。