Let, D=[d_1,d_2,\cdots,d_T] is a known vector.
t is an optimization variable, L of size T\times S is an binary optimization variable
R^{(1)},R^{(2)},\cdots,R^{(T)} are known matrices
Z^{(1)},Z^{(2)},\cdots,Z^{(T)} are optimization variables
Note that Z^{(p)} and R^{(p)} are of same size.
Z^{(1)} and Z^{(2)} can be of different sizes.
\begin{bmatrix} \left(\sum_{m=1}^{M_1}\sum_{n=1}^{N_1}Z^{(1)}_{m,n}R^{(1)}_{m,n}\right)L_{1,1} & \left(\sum_{m=1}^{M_1}\sum_{n=1}^{N_1}Z^{(1)}_{m,n}R^{(1)}_{m,n}\right)L_{1,2} & \cdots & \left(\sum_{m=1}^{M_1}\sum_{n=1}^{N_1}Z^{(1)}_{m,n}R^{(1)}_{m,n}\right)L_{1,S} \\ \left(\sum_{m=1}^{M_2}\sum_{n=1}^{N_2}Z^{(2)}_{m,n}R^{(2)}_{m,n}\right)L_{2,1} & \left(\sum_{m=1}^{M_2}\sum_{n=1}^{N_2}Z^{(2)}_{m,n}R^{(2)}_{m,n}\right)L_{2,2} & \cdots & \left(\sum_{m=1}^{M_2}\sum_{n=1}^{N_2}Z^{(2)}_{m,n}R^{(2)}_{m,n}\right)L_{2,S}\\ \left(\sum_{m=1}^{M_3}\sum_{n=1}^{N_3}Z^{(3)}_{m,n}R^{(3)}_{m,n}\right)L_{3,1} & \left(\sum_{m=1}^{M_3}\sum_{n=1}^{N_3}Z^{(3)}_{m,n}R^{(3)}_{m,n}\right)L_{3,2} & \cdots & \left(\sum_{m=1}^{M_3}\sum_{n=1}^{N_3}Z^{(3)}_{m,n}R^{(3)}_{m,n}\right)L_{3,S}\\ \vdots & \ddots & \cdots & \vdots\\ \left(\sum_{m=1}^{M_T}\sum_{n=1}^{N_T}Z^{(T)}_{m,n}R^{(T)}_{m,n}\right)L_{T,1} & \left(\sum_{m=1}^{M_T}\sum_{n=1}^{N_T}Z^{(T)}_{m,n}R^{(T)}_{m,n}\right)L_{T,2} & \cdots & \left(\sum_{m=1}^{M_T}\sum_{n=1}^{N_T}Z^{(T)}_{m,n}R^{(T)}_{m,n}\right)L_{T,S} \end{bmatrix}
Let the matrix above is defined as Q.
The constraint I have is
sum(Q,2)>=D.*t
Apart from the linearization (knowing the linearization technique), how can I express this in CVX?
Or
\begin{bmatrix} \left(\sum_{m=1}^{M_1}\sum_{n=1}^{N_1}Z^{(1)}_{m,n}R^{(1)}_{m,n}\right)L_{1,1} + \left(\sum_{m=1}^{M_1}\sum_{n=1}^{N_1}Z^{(1)}_{m,n}R^{(1)}_{m,n}\right)L_{1,2} + \cdots + \left(\sum_{m=1}^{M_1}\sum_{n=1}^{N_1}Z^{(1)}_{m,n}R^{(1)}_{m,n}\right)L_{1,S} \\ \left(\sum_{m=1}^{M_2}\sum_{n=1}^{N_2}Z^{(2)}_{m,n}R^{(2)}_{m,n}\right)L_{2,1} + \left(\sum_{m=1}^{M_2}\sum_{n=1}^{N_2}Z^{(2)}_{m,n}R^{(2)}_{m,n}\right)L_{2,2} + \cdots + \left(\sum_{m=1}^{M_2}\sum_{n=1}^{N_2}Z^{(2)}_{m,n}R^{(2)}_{m,n}\right)L_{2,S}\\ \left(\sum_{m=1}^{M_3}\sum_{n=1}^{N_3}Z^{(3)}_{m,n}R^{(3)}_{m,n}\right)L_{3,1} + \left(\sum_{m=1}^{M_3}\sum_{n=1}^{N_3}Z^{(3)}_{m,n}R^{(3)}_{m,n}\right)L_{3,2} +\cdots + \left(\sum_{m=1}^{M_3}\sum_{n=1}^{N_3}Z^{(3)}_{m,n}R^{(3)}_{m,n}\right)L_{3,S}\\ \vdots\\ \left(\sum_{m=1}^{M_T}\sum_{n=1}^{N_T}Z^{(T)}_{m,n}R^{(T)}_{m,n}\right)L_{T,1} +\left(\sum_{m=1}^{M_T}\sum_{n=1}^{N_T}Z^{(T)}_{m,n}R^{(T)}_{m,n}\right)L_{T,2} + \cdots + \left(\sum_{m=1}^{M_T}\sum_{n=1}^{N_T}Z^{(T)}_{m,n}R^{(T)}_{m,n}\right)L_{T,S} \end{bmatrix}
Let us define the vector above as q, the constraint I have is
q>=D.*t