On Finding a Generalized Lowest Rank Solution to a Linear Semi-definite Feasibility Problem

In this note, we generalize the affine rank minimization problem and the vector cardinality minimization problem and show that the resulting generalized problem can be solved by solving a sequence of continuous concave minimization problems. In the case of the vector cardinality minimization problem, we show that it can be solved by solving the continuous concave minimization problem.

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