I want to make the below constraints.

β_ππ‘βγγππγ*(ππ‘,π)βπΆ*(ππ‘,ππ) γ=0

π
πππ(C_(ππ‘,ππ) )= πΆπππ(π
π) β π
πππ(γππγ_(ππ‘,π)) = 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.

RankΒ© = 12

How do you think of the rank-constraint?

Iβm not sure whether or not C matrix is convex.