how to solve this problem using CVX :

for some positive lambda , where the norm of the first argument is the nuclear norm

and the mapping A is defined as :

the mapping is an affine mapping ofcourse and i can construct using a matlab code , and the matrix B has same dimension as A(x), i don’t know how to represent a general mapping from vector to matrix in CVX and for the first norm term we can separate it from the objective and make an SDP constraint