I want to make the below constraints.
𝑅𝑎𝑛𝑘(C_(𝑟𝑡,𝑙𝑑) )= 𝐶𝑎𝑟𝑑(𝑅𝑇) − 𝑅𝑎𝑛𝑘(〖𝑆𝑇〗_(𝑟𝑡,𝑖)) = 12
ST(rt, i) is known matrix,
and C(rt, ld) is unknown matrix (variable) which represents the dependence of row-vector(rt) in ST matrix.
Because rank of the ST matrix is already known, the number of elements in set C is also known (12).
From this aspect, in order to make sure the uniqueness (independence) of columns (ld) in C matrix, I set the rank constraint.
Rank© = 12
How do you think of the rank-constraint?
I’m not sure whether or not C matrix is convex.